Texas Instruments Titanium TI-89 User Manual Download Page 291

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Basic Function Graphing

288

Basic Function Graphing

Overview of Steps in Graphing Functions

To graph one or more

y(x)

functions, use the general steps shown below. For a detailed

description of each step, refer to the following pages. You may not need to do all the
steps each time you graph a function.

Graphing Functions

1. Set

Graph

mode (

) to

FUNCTION

Also set

Angle

mode, if necessary.

2. Define x and y components on Y= Editor

(

8 #

3. Select (

†

) which defined functions to

graph.

Note:

To turn off any stat data plots, press

‡

or use

†

to deselect them.

Summary of Contents for Titanium TI-89

Page 1: ...ng applications Modes Graphing a function Entering numbers Creating Tables Statistic Data Plots Matrices Split Screens Beyond the Basics Activities Archiving Unarchiving Programming Functions Instructions More Information Connectivity Text Editor Number Bases Support Service TI ...

Page 2: ...nce This equipment has been tested and found to comply with the limits for a Class B digital device pursuant to Part 15 of the FCC rules These limits are designed to provide reasonable protection against harmful interference in a residential installation This equipment generates uses and can radiate radio frequency energy and if not installed and used in accordance with the instructions may cause ...

Page 3: ...TI 89 Titanium iii Caution Any changes or modifications to this equipment not expressly approved by Texas Instruments may void your authority to operate the equipment ...

Page 4: ... are already installed and the AAA batteries are provided with the product 1 Remove the battery cover from the back of the calculator 2 Unwrap the four AAA batteries provided with your product and insert them in the battery compartment Arrange the batteries according to the polarity and diagram in the battery compartment 3 Replace the battery cover on the calculator The cover should snap into plac...

Page 5: ...desktop To avoid losing Apps do not remove the batteries during initialization You can re install Apps from either the Product CD ROM or education ti com Adjusting the contrast The Apps desktop The Apps desktop is the starting point for operating your TI 89 Titanium Your installed Apps appear on the Apps desktop as icons organized in categories for easy access From the Apps desktop you can Open Ap...

Page 6: ...me of the highlighted App View and edit the time and date Check status line information View split screen mode information TI 89 Titanium Apps desktop Ê View full name of highlighted App Ë View time and date Ì Press to open highlighted App Í Scroll down to view additional Apps Î Check status line information Ë Ì Ê Ï Î Í ...

Page 7: ... screen appears You can use either of the following keys to turn off the TI 89 Titanium Press Description 2 press 2 and then press Settings and memory contents are retained by the Constant Memory feature You cannot however use 2 if an error message is displayed When you turn the TI 89 Titanium on again it displays either the Home screen or the Apps desktop regardless of the last application you us...

Page 8: ... off automatically following several minutes of inactivity When you turn on the calculator after APD The display cursor and any error conditions are exactly the same as before APD All settings and memory contents are retained Note APD does not function when a calculation or program is in progress unless a pause is specified in the calculation or program ...

Page 9: ...Getting Started 6 TI 89 Titanium keys Ë Ì Í Ê ...

Page 10: ...special characters Use the CHAR Character menu and key commands to enter special characters The CHAR menu lets you access Greek math international and other special characters An on screen keyboard map shows the locations of shortcuts used to enter other commonly used characters To select characters from the CHAR menu 1 Press 2 G The CHAR menu appears 2 Use the cursor keys to select a category A s...

Page 11: ... the right arrow symbol in the Text Editor To open the keyboard map press 8 The keyboard map appears Press Result 2 G 4 9 or Press D repeatedly to select 9 and press Scroll down for more characters Symbol displayed at cursor location ...

Page 12: ...aracters press 2 and the corresponding key Press N to close the map Example Use the keyboard map to find the not equal to symbol ƒ shortcut and enter the symbol in the Program Editor Press Result 8 Á Symbol displayed at cursor location ...

Page 13: ...ctions are printed above their corresponding keys in the same color as the 2 key 8 Diamond Accesses Apps menu options and other operations Diamond functions are printed above their corresponding keys in the same color as the 8 key Shift Types an uppercase character for the next letter key you press Also used with A and B to highlight characters when editing j Alpha Lets you type alphabetic charact...

Page 14: ...pen Apps and select or edit Apps categories On the calculator Home screen open toolbar menus to select math related operations Within Apps open toolbar menus to select App options Numeric keypad The numeric keypad lets you enter positive and negative numbers To enter a negative number press before typing the number Note Don t confuse the negation key with the subtraction key Press Result 2 ...

Page 15: ... value can be an expression 2 Press 2 The exponent symbol í follows the numbers you entered 3 Type the exponent as an integer with up to three digits As the following example shows you can use a negative exponent Example On the calculator Home screen enter 0 00685 using scientific notation Press Result 6 8 5 3 ...

Page 16: ...able screen 5 6 7 These keys let you edit entered information by performing a cut copy or paste operation O Displays the Apps desktop 8 O With the Apps desktop off displays the FLASH APPLICATIONS menu 2 a Switches between the last two chosen Apps 2 Turns the custom menu on and off 2 4 Converts measurement units Designates a measurement unit 0 Deletes the character to the left of the cursor backspa...

Page 17: ...ert and overwrite modes 2 Displays the MEMORY screen Displays a list of commands 2 Recalls the contents of a variable Stores a value to a variable 2 G Displays the CHAR menu which lets you select Greek letters international accented characters and other special characters 2 K In full screen mode displays the Apps desktop In split screen mode displays the full screen view of the active App With the...

Page 18: ...nium mode settings 1 Press 3 Page 1 of the MODE dialog box appears 2 Press or to display the modes listed on Page 2 or Page 3 Note Modes that are grayed out are available only if other required mode settings are selected For example the Custom Units mode listed on Page 3 is available only if the Unit System mode is set to CUSTOM Viewing mode settings Press Result 3 ã ...

Page 19: ...Getting Started 16 Changing mode settings Example Change the Language mode setting to Spanish Español Press Result 3 Press Result ...

Page 20: ...the Language field D Press B and then press D until 3 Español is highlighted Note Your menu list might vary depending on the languages installed Note The previous open App appears in this example the calculator Home screen Press Result ...

Page 21: ...ly Commands not beginning with a letter are found at the end of the list etc The Catalog Help App includes details about each command Options not currently valid are grayed out For example the Flash Apps menu option is grayed out if no Flash applications are installed on your TI 89 Titanium the User Defined menu option is grayed out if you have not created a function or program Note Typing a lette...

Page 22: ...them to other Apps such as the Y Editor Text Editor or CellSheet Apps Example Insert the comDenom command on the calculator Home screen entry line Note Before selecting a command position the cursor where you want the command to appear displays Flash Apps commands if any displays User Defined commands if any Press Result ...

Page 23: ...e status line displays any required and optional parameters for the selected command Optional parameters appear in square brackets Note Pressing ƒ also displays the parameters for the selected command Press Result j C 2 D Then press D until the pointer is at the comDenom function ...

Page 24: ...ing point for math operations including executing instructions evaluating expressions and viewing results To display the calculator Home screen press 8 You can also display the calculator Home screen from the Apps desktop by highlighting the Home icon and pressing Selected command Command parameters Brackets indicate optional parameters ...

Page 25: ...and so on to display menus Ì Result of last entry is displayed here Note that results are not displayed on the entry line Í Status line shows the current state of the calculator Î Entry line displays your current entry Ï Your last entry is displayed here To return to the Apps desktop from the calculator Home screen press O Ê Ë Ï Î Í Ì ...

Page 26: ...hich normally rests on the entry line can be moved into the history area The following table shows you how to move the cursor around in the history area To Do this View entries answers scrolled off the screen From the entry line press C to highlight the last answer Continue using C to move the cursor from answer to entry through the history area Go to the oldest or newest entry answer pair If the ...

Page 27: ...he number of pairs that can be saved 1 From the calculator Home screen press ƒ and select 9 Format 2 Press B and use C or D to highlight the new number 3 Press To clear the history area and delete all saved pairs From the calculator Home screen press ƒ and select 8 Clear Home or Total number of pairs currently saved ________ 8 30 _______ Maximum number of pairs that can be saved Pair number of the...

Page 28: ...sktop icon is truncated use the cursor keys to highlight the icon Now view the full name at the top of the Apps desktop Opening Apps Use the cursor keys to highlight the Apps icon on the Apps desktop and press The App either opens directly or displays a dialog box The most common dialog box lists these options for the App Note The TI 89 Titanium uses the general term variable to refer to the App d...

Page 29: ...ion enter any required information and press The App appears Example Create a new program using the Program Editor New Creates a new file with the name typed in the field Press Result Use cursor keys to highlight 3 Option Description ...

Page 30: ... Press O The icons for the last Apps category selected appear on the Apps desktop with the icon for the last App opened highlighted You can also return to the Apps desktop by pressing 2 K in full screen mode In split screen mode press 2 K twice To return to the last open App from the Apps desktop press 2 a D D p r o g r a m 1 Press Result ...

Page 31: ...f necessary The App icons for the selected category appear on the Apps desktop The App icons for the selected category appear on the Apps desktop Key Description All Icons for all installed Apps displayed Not customizable English Customizable category English is the default SocialSt Customizable category SocialSt social studies is the default Math Customizable category Math is the default 2 ˆ Grap...

Page 32: ...tegories on page 29 Press or N to clear the message and return to the Apps desktop Customizing the Apps categories The TI 89 Titanium organizes your Apps into seven categories six of which you can customize to fit your individual needs The All category contains every installed App and cannot be edited To customize the through 2 Š Apps categories 1 Select ƒ 1 Edit Categories A submenu displays the ...

Page 33: ... eight characters including letters with or without capitalization numbers punctuation and accented characters 4 To add or remove an App shortcut from the category press D as required to highlight the box next to the App then press B to add or remove the check mark 9 5 To save the changes and return to the Apps desktop press Example Replace the Social Studies category with the Business category an...

Page 34: ...Getting Started 31 2 or D 2 B u s i n e s s D B D B Press Result ...

Page 35: ...or example view the Y Editor and Graph screens simultaneously to see the list of functions and how they are graphed Select the Split Screen mode from Page 2 of the MODE screen The TI 89 Titanium displays the selected Apps in the split screen view as shown Split the screen horizontally top bottom or vertically left right Press Result ...

Page 36: ...s and the portions of the screen in which each is displayed The highlighted numeral indicates the split screen portion where the next App you open will appear Note The Apps desktop always appears in the full screen view Top bottom split screen Split screen status highlight indicates the portion where the next App selected will open Names of open Apps ...

Page 37: ...ndicator Meaning Ê Current folder Name of the selected folder MAIN is the default folder Ë Modifier key Selected modifier key 2 8 7 if any Ì Angle mode Selected units in which angle values are displayed and interpreted RAD DEG Í Exact Approx mode Mode in which answers are calculated and displayed AUTO EXACT APPROX Î Graph number Active of two independent graphs in split screen mode GR 1 GR 2 Ï Gra...

Page 38: ... answer pairs default is 30 maximum is 99 in the history area of the calculator Home screen Ñ Replace batteries Displayed when batteries are low BATT If BATT is highlighted with a black background change the batteries as soon as possible Ò Busy Pause Locked Archived variable BUSY Calculation or graph is in progress PAUSE You paused a graph or program Œ Variable opened in the current editor is lock...

Page 39: ...de field To return to the Apps desktop from the calculator Home screen press O Using the clock Use the CLOCK dialog box to set the time and date select the clock display format and turn the clock off and on D D B C Note The previous open App appears in this example the calculator Home screen Press Result ...

Page 40: ...rmat field highlighted Note Because the CLOCK dialog box displays the settings current at the time you open the dialog box you might need to update the time before exiting Setting the time 1 Press B to open the list of time formats 2 Press C or D to highlight an option then press The selected format appears in the Time Format field 3 Press D to highlight the Hour field 4 Type the hour then press D...

Page 41: ... press The time is updated in the top right corner of the Apps desktop Setting the date 1 Press C or D as required to highlight the Date Format field 2 Press B to open the list of date formats 3 Press C or D to highlight an option then press The selected format appears in the Date Format field 4 Press D to highlight the Year field 5 Type the year then press D to highlight the Month field 6 Press B...

Page 42: ...hen press to save your settings and exit The date is updated in the top right corner of the Apps desktop Example Set the time and date to 19 10 02 October 19 2002 at 1 30 p m Press Result Use cursor keys to highlight D 1 D Time and date ...

Page 43: ...Getting Started 40 3 0 D B D D B D Press Result ...

Page 44: ...Getting Started 41 D 2 0 0 2 D B Scroll down to October and press Press Result ...

Page 45: ...Getting Started 42 Turning off the clock From the Apps desktop open the CLOCK dialog box and select OFF in the Clock field D 1 9 Press Result Revised time and date ...

Page 46: ...Getting Started 43 Example Turn off the clock Press Result Use cursor keys to highlight Scroll down to the Clock field B C Clock on ...

Page 47: ...ding to the toolbars at the top of the calculator Home screen and most App screens Select other menus using key commands Toolbar menus The starting point for TI 89 Titanium math operations the calculator Home screen displays toolbar menus that let you choose math related options Toolbar menus also appear at the top of most App screens These menus list common functions of the active App Press Resul...

Page 48: ...ast menu option is selected press D to select the first option on the menu Press To display 2 G CHAR menu Lists characters not available on the keyboard characters are organized by category Greek math punctuation special and international 2 I MATH menu Lists math operations by category O APPLICATIONS menu Lists the installed Apps Menu is available only when the Apps desktop is turned off Apps are ...

Page 49: ...6 Example Select factor from the Algebra menu on the calculator Home screen Press Result Press or From the Apps desktop use the cursor keys to highlight and press 2 or D 6 indicates Algebra menu will open when you press ...

Page 50: ...enu options A small arrow symbol ú to the right of a menu option indicates that selecting the option will open a submenu Example Select ord from the MATH menu on the calculator Home screen Press Result 2 I points to additional options ...

Page 51: ...Getting Started 48 Using dialog boxes An ellipsis at the end of a menu option indicates that choosing the option will open a dialog box Select the option and press C or C C B B or C Press Result ...

Page 52: ... the Window Editor Note Pressing the 8 S key shortcut also opens the SAVE COPY AS dialog box in most Apps Press Result O Use the cursor keys to highlight and press ƒ 2 or D N Press B to display a list of folders Type the name of the variable Press twice to save and ...

Page 53: ... will appear instead of the next toolbar menu Press B again to move to the next menu More information is available about menus See the electronic Operating the Calculator chapter Custom menu The custom menu provides quick access to your most commonly used options Use the default custom menu or create your own using the Program Editor You can include any available TI 89 Titanium command or characte...

Page 54: ...Getting Started 51 Example Turn on and turn off the custom menu from the calculator Home screen Example Restore the default custom menu Press Result 2 F 2 F Default custom menu Normal toolbar menu ...

Page 55: ...lt custom menu erases the previous custom menu If you created the previous custom menu with a program you can run the program again to reuse the menu Press Result 2 F to turn off the custom menu and turn on the standard toolbar menu 2 ˆ 3 or D D ...

Page 56: ...NS menu to open Apps To open the APPLICATIONS menu with the Apps desktop off press O Note If you press O with the Apps desktop turned on the Apps desktop will appear instead of the APPLICATIONS menu Example With the Apps desktop turned off open the Window Editor from the APPLICATIONS menu Press Result O Press Result ...

Page 57: ...they are graphed Setting split screen mode You can split the screen either top to bottom or left to right from the MODE dialog box The split screen setting stays in effect until you change it 1 Press 3 to display the MODE dialog box 2 Press to display the Split Screen mode setting 3 Press B to open the Split Screen mode menu 4 Press D as required to highlight either TOP BOTTOM or LEFT RIGHT 5 Pres...

Page 58: ...Getting Started 55 Example Set split screen mode to TOP BOTTOM Press Result 3 B D ...

Page 59: ...de additional mode settings become available Mode Description Split 2 App Lets you specify the App displayed in the bottom or right portion of the split screen Works together with Split 1 App which lets you specify the App displayed in the top or left portion of the split screen Press Result Full screen mode Split screen mode ...

Page 60: ...vailable Apps See Setting split screen mode on page 54 2 Press D or C to highlight the App and press 3 Repeat steps 1 and 2 for the Split 2 App mode setting Example Display the Y Editor in the top screen and the Graph App in the bottom screen Number of Graphs Lets you set up and display two independent graphs Press Result D B 2 Mode Description ...

Page 61: ... same nongraphing App or to the same graphing App with Number of Graphs set to 1 the TI 89 Titanium exits split screen mode and displays the App in full screen mode Selecting the active App In split screen mode only one App can be active at a time D B 4 Press Result ...

Page 62: ...alculator Home screen Pressing 2 K again turns off the split screen mode and displays the calculator Home screen in full screen mode Select Split Screen on Page 2 of the MODE dialog box set split screen mode to FULL and press Press 2 K twice to display the Apps desktop More information is available about using split screens See the electronic Split Screens chapter Managing Apps and operating syste...

Page 63: ...ons see the TI E PS Web site Before downloading Apps to your TI 89 Titanium please read the license agreement on the CD ROM or TI Web site Finding the OS version and identification ID numbers If you purchase software from the TI E PS Web site or call the customer support number you will be asked to provide information about your TI 89 Titanium You will find this information on the ABOUT screen To ...

Page 64: ...t than the one shown above Deleting an Application Deleting an application removes it from the TI 89 Titanium and increases space for other applications Before deleting an application consider storing it on a computer for reinstallation later 1 Quit the application 2 Press 2 to display the VAR LINK All screen 3 Press 2 to display the list of installed applications 4 Select the application you want...

Page 65: ...lator Use the USB unit to unit cable or an I O unit to unit cable to connect the TI 89 Titanium to a compatible graphing calculator or peripheral device such as a TI 89 or TI 92 Plus graphing calculator or the CBL 2 and CBR systems To show your calculator s display to the classroom Use the accessory port to connect the TI Presenter video adapter to the teacher model of the TI 89 Titanium The TI Pr...

Page 66: ...lkaline batteries and a backup silver oxide battery SR44SW or 303 The backup battery is already installed and the AAA batteries are provided with your product I O port USB port TI 89 Titanium ports Accessory port I O port USB port TI 89 Titanium ports teacher model ...

Page 67: ...ity and diagram in the battery compartment 3 Replace the battery cover on the calculator The cover should snap into place Replacing the AAA alkaline batteries As the batteries lose power the display begins to dim especially during calculations If you find yourself increasing the contrast frequently replace the AAA alkaline batteries The status line also gives battery information Indicator Meaning ...

Page 68: ... back up battery and the AAA alkaline batteries at the same time Replacing the backup silver oxide battery 1 To replace the silver oxide backup battery remove the battery cover and unscrew the tiny screw holding the BACK UP BATTERY cover in place 2 Remove the old battery and install a new SR44SW or 303 battery positive side up Replace the cover and the screw ...

Page 69: ...errupt the transfer before it is complete you will need to reinstall the OS via a computer Again remember to install new batteries before downloading Please contact Texas Instruments as described in Service Support Information if you experience a problem Battery Precautions Take these precautions when replacing batteries Do not leave batteries within the reach of children Do not mix new and used b...

Page 70: ...Getting Started 67 ...

Page 71: ...Titanium The history area in each screen was cleared by pressing ƒ and selecting 8 Clear Home before performing each example to illustrate only the results of the example s keystrokes Showing Computations Steps and keystrokes Display Compute sin p 4 and display the result in symbolic and numeric format To clear the history area of previous calculations press ƒ and select 8 Clear Home 2 W 2 T e 4 d...

Page 72: ... several numbers to see how the TI 89 Titanium handles very large integers To get the factorial operator press 2 I select 7 Probability and then select 1 5 2 I 7 1 20 2 I 7 1 30 2 I 7 1 Steps and keystrokes Display Compute 3 5i 3 to see how the TI 89 Titanium handles computations involving complex numbers Press c 3 5 2 d Z 3 ...

Page 73: ...y line by typing FACTOR on the keyboard or by pressing and selecting 2 factor Press 2 2634492 d Optional Enter other numbers on your own Steps and keystrokes Display Expand the expression xN5 3 You can enter expand on the entry line by typing EXPAND on the keyboard or by pressing and selecting 3 expand Press 3 c X 5 d Z 3 d Optional Enter other expressions on your own ...

Page 74: ...enter propFrac on the entry line by typing PROPFRAC on the keyboard or by pressing and selecting 7 propFrac Press 7 c X Z 2 2 X 5 d e c X 1 d d Steps and keystrokes Display Factor the polynomial x2 N5 with respect to x You can enter factor on the entry line by typing FACTOR on the keyboard or by pressing and selecting 2 factor Press 2 X Z 2 5 b X d ...

Page 75: ... solve from the Catalog menu by typing SOLVE on the keyboard or by pressing and selecting 1 solve The status line area shows the required syntax for the marked item in the Catalog menu Press 1 X Z 2 2 X 6 Á 2 b X d Steps and keystrokes Display Solve the equation x2 N2xN6 2 with respect to x where x is greater than zero The with I operator provides domain constraint 1 X Z 2 2 X 6 Á 2 b X d Í X 2 Ã ...

Page 76: ...n for x into the second Steps and keystrokes Display Find the derivative of xNy 3 x y 2 with respect to x This example illustrates using the calculus differentiation function and how the function is displayed in pretty print in the history area Press 2 c X Y d Z 3 e c X Y d Z 2 b X d Steps and keystrokes Display Find the integral of x sin x with respect to x This example illustrates using the calc...

Page 77: ...nu You can also type solve directly from the keyboard or select it from the Catalog M M 1 2 X 3 Y Á 4 b X d 2 Begin to solve the equation Lx 7y L12 for y but do not press yet Press 1 X 7 Y Á 12 b Y d 3 Use the with operator to substitute the expression for x that was calculated from the first equation This gives the value of y The with operator is displayed as on the screen Use the auto paste feat...

Page 78: ...m a calculate the force when m 5 kilograms and a 20 meters second2 What is the force when a 9 8 meters second2 This is the 4 Highlight the equation for x in the history area Press C C C 5 Auto paste the highlighted expression to the entry line Then substitute the value of y that was calculated from the second equation Í C The solution is x L8 11 and y L20 11 Steps and keystrokes Display ...

Page 79: ...ess 3 B 1 2 Create an acceleration unit for meters second2 named _ms2 The UNITS dialog box lets you select units from an alphabetical list of categories You can use 2 D and 2 C to scroll one page at a time through the categories If you use the UNITS dialog box to select a unit the _ is entered automatically Now instead of re entering _m _s2 each time you need it you can use _ms2 Also you can now u...

Page 80: ... 20 meters second2 _ms2 If you know the abbreviation for a unit you can type it from the keyboard 5 8 5 2 KG j p 20 8 5 2 MS j 2 4 Using the same m calculate the force for an acceleration due to gravity the constant _g For _g you can use the pre defined constant available from the UNITS dialog box or you can type _g 5 8 5 2 KG j p 2 À B j G 5 Convert to kilograms of force _kgf 2 4 displays the 4 c...

Page 81: ...ng capabilities of the TI 89 Titanium by graphing the function y x2N3 N10 2 Steps and keystrokes Display 1 Display the Y Editor Press 8 2 Enter the function abs x2 N3 N10 2 The screen shot shows the pretty print display at y1 c A X Z 2 3 d 1 0 d e 2 3 Display the graph of the function Select 6 ZoomStd by pressing 6 or by moving the cursor to 6 ZoomStd and pressing Press 6 entry line ...

Page 82: ...wer bound Press B right cursor to move the tracing cursor until the lower bound for x is just to the left of the minimum node before pressing the second time Press B B 7 Set the upper bound Press B right cursor to move the tracing cursor until the upper bound for x is just to the right of the minimum node Press B B Steps and keystrokes Display tracing cursor ...

Page 83: ...Std Then use ZoomSqr to adjust the viewing window 8 Find the minimum point on the graph between the lower and upper bounds Press 9 Transfer the result to the Home screen and then display the Home screen 8 Steps and keystrokes Display 1 Display the MODE dialog box For Graph mode select FUNCTION Press 3 B 1 Steps and keystrokes Display minimum point minimum coordinates ...

Page 84: ... function graphing you must define separate functions for the top and bottom halves of a circle 8 8 2 j R Z 2 X Z 2 d 4 Define y2 x the function for the bottom half of the circle The bottom half is the negative of the top half so you can define y2 x Ly1 x Use the full function name y1 x not simply y1 Press Y 1 c X d Steps and keystrokes Display 5 r r2 x2 r2 x2 ...

Page 85: ...ed at an angle q of 60 with an initial velocity v0 of 15 meters sec The gravity constant g 9 8 meters sec2 5 Select the ZoomStd viewing window which automatically graphs the functions In the standard viewing window both the x and y axes range from L10 to 10 However this range is spread over a longer distance along the x axis than the y axis Therefore the circle appears as an ellipse Press 6 6 Sele...

Page 86: ...ess 3 B 2 2 Display and clear the Y Editor Then define the horizontal component xt1 t v0t cos q Enter values for v0 and q 8 8 15T p 2 X 60 2 d Type T p 2 X not T 2 X Enter a symbol by typing either 2 or 2 I 2 1 This ensures a number is interpreted as degrees regardless of the angle mode 3 Define the vertical component yt1 t v0t sin q N g 2 t2 Enter values for v0 q and g 15T p 2 W 60 2 d c 9 8 e 2 ...

Page 87: ...lue and move to the next variable Press 8 0 D 3 D 02 D 2 D 25 D 5 D 2 D 10 D 5 5 Graph the parametric equations to model the path of the ball Press 8 6 Select Trace Then move the cursor along the path to find the y value at maximum height t value where the ball hits the ground Press B or A as necessary Steps and keystrokes Display ...

Page 88: ...explore the appearance of the rose for other values of A and B Steps and keystrokes Display 1 Display the MODE dialog box For Graph mode select POLAR For Angle mode select RADIAN Press 3 B 3 D D D B 1 2 Display and clear the Y Editor Then define the polar equation r1 q A sin Bq Enter 8 and 2 5 for A and B respectively 8 8 8 2 W 2 5 8 Ï d ...

Page 89: ...emaining petals have q values greater than 2p The rose does not appear symmetrical Both the x an y axes range from L10 to 10 However this range is spread over a longer distance along the x axis than the y axis Press 6 4 Display the Window Editor and change qmax to 4p 4p will be evaluated to a number when you leave the Window Editor Press 8 D 4 2 T Steps and keystrokes Display ...

Page 90: ...e end of each year Does it stabilize at a certain number 5 Select ZoomSqr which regraphs the equation ZoomSqr increases the range along the x axis so that the graph is shown in correct proportion Press 5 You can change values for A and B as necessary and regraph the equation Initially After 1 Year After 2 Years After 3 Years 4000 8 x 4000 1000 8 x 8 x 4000 1000 1000 8 x 8 x 8 x 4000 1000 1000 1000...

Page 91: ...ake the integer part of the result No fractional trees are harvested To access iPart you can use 2 I simply type it or select it from the CATALOG 8 8 2 I 14 8 j U1 c j N 1 d 1000 d 3 Define ui1 as the initial value that will be used as the first term Press 4000 4 Display the Window Editor Set the n and plot Window variables nmin 0 and nmax 50 evaluate the size of the forest over 50 years Press 8 0...

Page 92: ...ss 8 7 Select Trace Move the cursor to trace year by year How many years nc does it take the number of trees yc to stabilize Trace begins at nc 0 nc is the number of years xc nc since n is plotted on the x axis yc u1 n the number of trees at year n Press B and A as necessary Steps and keystrokes Display By default sequences use the Square display style ...

Page 93: ... Steps and keystrokes Display 1 Display the MODE dialog box For Graph mode select 3D Press 3 B 5 2 Display and clear the Y Editor Then define the 3D equation z1 x y x3 y N y3 x 390 Notice that implied multiplication is used in the keystrokes Press 8 8 c X Z 3 Y Y Z 3 X d e 390 3 Change the graph format to display and label the axes Also set Style WIRE FRAME You can animate any graph format style b...

Page 94: ...en you animate the graph the screen returns to normal view automatically Except for animation you can do the same things in normal and expanded view Press p press p to switch between expanded and normal view 5 Animate the graph by decreasing the eyef Window variable value D or C may affect eyeq and eyeψ but to a lesser extent than eyef To animate the graph continuously press and hold the cursor fo...

Page 95: ...he viewing orbit around the graph Press 0 zero not the letter O A A A 7 View the graph along the x axis the y axis and then the z axis Press X This graph has the same shape along the y axis and x axis Press Y Press Z 8 Return to the initial orientation Press 0 zero Steps and keystrokes Display ...

Page 96: ... the graph in different graph format styles Í press Í to switch from each style to the next HIDDEN SURFACE CONTOUR LEVELS may require extra time to calculate contours WIRE AND CONTOUR WIRE FRAME Steps and keystrokes Display ...

Page 97: ...plot is not displayed Differential Equation Graphing Graph the solution to the logistic 1st order differential equation y 001y 100Ny Start by drawing only the slope field Then enter initial conditions in the Y Editor and interactively from the Graph screen Steps and keystrokes Display 1 Display the MODE dialog box For Graph mode select DIFF EQUATIONS Press 3 B 6 ...

Page 98: ...n call Leave the initial condition yi1 blank Note With y1 selected the device will graph the y1 solution curve not the derivative y1 Press 8 8 001 Y1 p c 100 Y1 d 3 Display the GRAPH FORMATS dialog box Then set Axes ON Labels ON Solution Method RK and Fields SLPFLD Note To graph one differential equation Fields must be set to SLPFLD or FLDOFF If Fields DIRFLD an error occurs when you graph 8 Í D D...

Page 99: ...only the slope field is drawn as specified by Fields SLPFLD in the GRAPH FORMATS dialog box Press 8 6 Return to the Y Editor and enter an initial condition yi1 10 Press 8 10 7 Return to the Graph screen Initial conditions entered in the Y Editor always occur at t0 The graph begins at the initial condition and plots to the right Then it plots to the left Press 8 Steps and keystrokes Display The ini...

Page 100: ... When selecting an initial condition interactively you can specify a value for t other than the t0 value entered in the Y Editor or Window Editor Instead of entering t and y1 after pressing 2 Š you can move the cursor to a point on the screen and then press You can use to trace curves for initial conditions specified in the Y Editor However you cannot trace the curve for an initial condition selec...

Page 101: ... select FUNCTION For Angle mode select RADIAN Press 3 B 1 D D D B 1 2 Display the Home screen Use the Graph command and the when function to specify the piecewise defined function 2 selects Graph from the Other toolbar menu and automatically adds a space 2 2 WHEN j c X 2 Â 0 b X b 5 p 2 X X d d 3 Execute the Graph command which automatically displays the Graph screen The graph uses the current Win...

Page 102: ...f the graph Use PIC1 as the variable name for the picture Be sure to set Type Picture By default it is set to GDB 2 B 2 D D PIC j 1 6 Clear the drawn horizontal line You can also press to regraph 2 ˆ 1 7 Open the saved picture variable to redisplay the graph with the line Be sure to set Type Picture By default it is set to GDB Press 1 B 2 if not already shown also set Variable pic1 Steps and keyst...

Page 103: ...e and where do they occur Steps and keystrokes Display 1 Display the MODE dialog box For the Graph mode select FUNCTION Press 3 B 1 2 Display and clear the Y Editor Then define y1 x x3 N 2x Press 8 8 X Z 3 2 X 3 Set the table parameters to tblStart M10 tbl 1 Graph Table OFF Independent AUTO Press 8 10 D 1 D B 1 D B 1 ...

Page 104: ...e table Notice that y1 changes sign at x M1 1 and 2 To scroll one page at a time use 2 D and 2 C Press D and C as necessary 6 Zoom in on the sign change between x L2 and x L1 by changing the table parameters to tblStart L2 tbl 1 Press 2 D 1 Steps and keystrokes Display ...

Page 105: ... the MODE dialog box For Graph select FUNCTION For Split Screen select LEFT RIGHT For Split 1 App select Y Editor For Split 2 App select Graph Press 3 B 1 B 3 D B 2 D B 4 2 Clear the Y Editor and turn off any stat data plots Then define y1 x 1x3N2x 6 A thick border around the Y Editor indicates it is active When active its entry line goes all the way across the display Press 8 5 1 X Z 3 2 X 6 ...

Page 106: ...h to the Y Editor Then edit y1 x to change 1x3 to 5x3 2 a is the second function of O The thick border is around the Y Editor Press 2 a C A B B 0 5 5 Switch to the Graph screen which regraphs the edited function The thick border is around the Graph screen Press 2 a 6 Switch to the Y Editor Then open the Window Editor in its place Press 2 a 8 Steps and keystrokes Display ...

Page 107: ...t variable which can have only one column is automatically converted into a data variable which can have multiple columns 7 Open the Home screen Then exit to a full sized Home screen Press 2 K twice Steps and keystrokes Display 1 Use O to display the Data Matrix Editor Create a new list variable named TEMP Press 3 B 3 D D TEMP Steps and keystrokes Display ...

Page 108: ... 5 6 C 3 Move to column 2 and define its column header so that it is twice the value of column 1 DATA is shown in the upper left corner to indicate that the list variable was converted to a data variable B 2 p j C 1 4 Move to the column 2 header cell to show its definition in the entry line When the cursor is on the header cell you do not need to press to define it Simply begin typing the expressi...

Page 109: ...t relates population to the number of buildings with more than 12 stories Using Median Median and linear regression calculations find and plot equations to fit the data For each regression equation predict how many buildings of more than 12 stories you would expect in a city of 300 000 people 5 Clear the contents of the variable Simply clearing the data does not convert the data variable back into...

Page 110: ...reate a new data variable named BUILD Press 3 D D BUILD 3 Using the sample data below enter the population in column 1 Pop in 1000s Bldgs 12 stories 150 4 500 31 800 42 250 9 500 20 750 55 950 73 Press 150 500 800 250 500 750 950 Steps and keystrokes Display ...

Page 111: ...es the cursor up one cell B 8 C 4 31 42 9 20 55 73 5 Move the cursor to row 1 in column 1 r1c1 Sort the data in ascending order of population This sorts column 1 and then adjusts all other columns so that they retain the same order as column 1 This is critical for maintaining the relationships between columns of data To sort column 1 the cursor can be anywhere in column 1 This example has you pres...

Page 112: ...he calculation to display the MedMed regression equation As specified on the Calculate dialog box this equation is stored in y1 x Press 8 Close the STAT VARS screen The Data Matrix Editor displays Press 9 Display the Calculate dialog box Set Calculation Type LinReg x C1 y C2 Store RegEQ to y2 x Press B 5 D D D B D Steps and keystrokes Display ...

Page 113: ...VARS screen The Data Matrix Editor displays Press 12 Display the Plot Setup screen Plot 1 is highlighted by default lets you clear highlighted Plot settings Press 13 Define Plot 1 as Plot Type Scatter Mark Box x C1 y C2 Notice the similarities between this and the Calculate dialog box B 1 D B 1 D C j 1 D j C2 Steps and keystrokes Display ...

Page 114: ...e display style to Dot Note Depending on the previous contents of your Y Editor you may need to move the cursor to y1 PLOTS 1 at the top of the screen means that Plot 1 is selected Notice that y1 x and y2 x were selected when the regression equations were stored 8 2 ˆ 2 16 Scroll up to highlight Plot 1 The displayed shorthand definition is the same as on the Plot Setup screen Press C Steps and key...

Page 115: ...n to the current session of the Data Matrix Editor Press 2a 19 Enter a title for column 3 Define column 3 s header as the values predicted by the MedMed line To enter a title the cursor must highlight the title cell at the very top of the column lets you define a header from anywhere in a column When the cursor is on a header cell pressing is not required B B C C 2 MED j Y1 c j C1 d Steps and keys...

Page 116: ... Define column 5 s header as the values predicted by the LinReg line B C C 2 LIN j Y2 c j C1 d 22 Enter a title for column 6 Define column 6 s header as the residuals for LinReg B C 2 RESID j j C2 j C5 23 Display the Plot Setup screen and deselect Plot 1 Press 24 Highlight Plot 2 and define it as Plot Type Scatter Mark Box x C1 y C4 MedMed residuals D D D C j 1 D j C4 Steps and keystrokes Display ...

Page 117: ...D C j 1 D j C6 26 Display the Y Editor and turn all the y x functions off From select 3 Functions Off not 1 All Off Plots 2 and 3 are still selected Press 8 3 27 Use ZoomData to graph the residuals marks the MedMed residuals marks the LinReg residuals Press 9 28 Display the Home screen Steps and keystrokes Display ...

Page 118: ... x 300 300 000 population The round function 2 I 1 3 ensures that results show an integer number of buildings After calculating the first result edit the entry line to change y1 to y2 Press 2 I 1 3 Y1 c 300 d b 0 d B A eight times 0 2 Steps and keystrokes Display 1 Use O to display the Program Editor Create a new program Press 3 2 Type PROG1 with no spaces as the name of the new program variable D...

Page 119: ...116 3 Display the template for a new program The program name Prgm and EndPrgm are shown automatically After typing in an input box such as Variable you must press twice Press twice Steps and keystrokes Display ...

Page 120: ...numeric expression 0 temp Creates a variable named temp and initializes it to 0 For i 1 n 1 Starts a For loop based on variable i First time through the loop i 1 At end of loop i is incremented by 1 Loop continues until i n temp i temp Adds current value of i to temp EndFor Marks the end of the For loop Disp temp Displays the final value of temp Type the program lines as shown Press at the end of ...

Page 121: ...the displayed dialog box Press 5 7 Continue with the program The Disp command displays the result on the Program I O screen The result is the sum of the integers from 1 through 5 Although the Program I O screen looks similar to the Home screen it is for program input and output only You cannot perform calculations on the Program I O screen Press twice Steps and keystrokes Display prog1 Output from...

Page 122: ...you want As you type practice moving the text cursor and correcting any typos you may enter 8 Leave the Program I O screen and return to the Home screen You can also press N 2 K or to return to the Home screen Press Steps and keystrokes Display 1 Start a new session of the Text Editor Press 3 Steps and keystrokes Display ...

Page 123: ...ess D TEST 3 Type some sample text To type a single uppercase letter press 7 and then the letter To type a space press j alpha function of the key To type a period press j to turn alpha lock off press and then press 2 to turn alpha lock on again Practice editing your text by using The cursor pad to move the text cursor 0 or 8 to delete the character to the left or right of the cursor respectively ...

Page 124: ...splay the Home screen Your text session was stored automatically as you typed Therefore you do not need to save the session manually before exiting the Text Editor 5 Return to the current session on the Text Editor Notice that the displayed session is exactly the same as you left it Press 2a Steps and keystrokes Display 1 Use O to display the Numeric Solver Steps and keystrokes Display ...

Page 125: ...g before you can define a in terms of g Accept the default for bound If a variable has been defined previously its value is shown as a default D 10 D D 9 8 C C C j G e 3 4 Move the cursor to the unknown variable m1 Optionally you can enter an initial guess for m1 Even if you enter a value for all variables the Numeric Solver solves for the variable marked by the cursor Press D D g 3 is evaluated w...

Page 126: ...arks the calculated values 6 Graph the solution using a ZoomStd viewing window The graph is displayed in a split screen You can explore the graph by tracing zooming etc The variable marked by the cursor unknown variable m1 is on the x axis and left rt is on the y axis Press 3 7 Return to the Numeric Solver and exit the split screen You can press or D to redisplay the list of variables Press 2 a 2 ...

Page 127: ...ox Page 2 For Base mode select DEC as the default number base Integer results are displayed according to the Base mode Fractional and floating point results are always displayed in decimal form Press 3 use D to move to Base mode B 1 2 Calculate 0b10 0hF 10 To enter a binary or hex number you must use the 0b or 0h prefix zero and the letter B or H Otherwise the entry is treated as a decimal number ...

Page 128: ... 2 4 2 HEX j 5 Add 1 to the result and leave it in the default decimal base Results use the 0b or 0h prefix to identify the base Press 1 6 Change the Base mode to HEX When Base HEX or BIN the magnitude of a result is restricted to certain size limitations Press 3 use D to move to Base mode B 2 7 Calculate 0b10 0hF 10 0 j B 10 0 2 HF j 10 Steps and keystrokes Display ...

Page 129: ...screen to view a list of the defined variables Then move a variable to the user data archive memory and explore the ways in which you can and cannot access an archived variable Archived 8 Change the Base mode to BIN Press 3 use D to move to Base mode B 3 9 Re enter 0b10 0hF 10 Press Steps and keystrokes Display ...

Page 130: ...n variables with the following variable types Expression 5 x1 Function x2 4 f x List 5 10 l1 Matrix 30 25 m1 M 5 9 X1 X Z 2 4 9 j F c X d 2 5 b 10 2 9 j L1 2 g 30 b 25 2 h 9 j M1 2 Suppose you start to perform an operation using a function variable but can t remember its name Press 5 p 3 Display the VAR LINK screen This example assumes that the variables assigned above are the only ones defined Pr...

Page 131: ... all different types Press D D B 5 5 Highlight the f function variable and view its contents Notice that the function was assigned using f x but is listed as f on the screen D 2 ˆ 6 Close the Contents window Press N 7 With the f variable still highlighted close VAR LINK and paste the variable name to the entry line Notice that is pasted Press 8 Complete the operation Press 2 d Steps and keystrokes...

Page 132: ... view is no longer in effect The screen lists all defined variables Press 2 use D to highlight x1 2 Use the Manage toolbar menu to archive the variable û indicates the variable is archived Press 8 3 Return to the Home screen and use the archived variable in a calculation 6 p X1 4 Attempt to store a different value to the archived variable Press 10 9 X1 ...

Page 133: ...Cancel the error message Press N 6 Use VAR LINK to unarchive the variable Press 2 use D to highlight x1 9 7 Return to the Home screen and store a different value to the unarchived variable Steps and keystrokes Display ...

Page 134: ...tes items that are selected Notice that this also selected the MAIN folder Note Instead of using if you don t want to delete all your variables you can select individual variables Highlight each variable to delete and press Press 1 2 Use to delete Note You can press 0 instead of 1 to delete the marked variables Press 1 3 Confirm the deletion Press ...

Page 135: ...der Acknowledge the message When VAR LINK is redisplayed the deleted variables are not listed Press 5 Close VAR LINK and return to the current application Home screen in this example When you use N instead of to close VAR LINK the highlighted name is not pasted to the entry line Press N Steps and keystrokes Display ...

Page 136: ...long battery life the APD Automatic Power Down feature lets the calculator turn itself off automatically Turning the Calculator On Press If you turned the unit off by pressing 2 the unit returns to either the Apps desktop or the Home screen If you turned the unit off by pressing 8 or if the unit turned itself off through APD the unit returns to whichever application you used last ...

Page 137: ...lay cursor and any error conditions are exactly as you left them All settings and memory contents are retained Press Description 2 press 2 and then press Settings and memory contents are retained by the Constant Memory feature However You cannot use 2 if an error message is displayed When you turn the calculator on again it displays either the Home screen or the Apps desktop regardless of the last...

Page 138: ...isplay contrast The contrast setting is retained in memory when the graphing calculator is turned off Adjusting the Display Contrast You can adjust the display contrast to suit your viewing angle and lighting conditions Contrast keys If you press and hold 8 or 8 too long the display may go completely black or blank To make finer adjustments hold 8 and then tap or To Press and hold both Decrease li...

Page 139: ...replace the four alkaline batteries Note The display may be very dark after you change batteries Use 8 to lighten the display The status line along the bottom of the display also gives battery information The TI 89 Titanium Keyboard Most keys can perform two or more functions depending on whether you first press a modifier key Indicator in status line Description Batteries are low Replace batterie...

Page 140: ...sed with 8 Ë 2 8 and j add functionality by increasing the available key commands Ì X Y and Z are often used in symbolic calculations Í A B C and D move the cursor Î O lets you select an application Ï evaluates an expression executes an instruction selects a menu item etc Í Î Ï Ê Ë Ì ...

Page 141: ...cesses the second function of the next key you press On the keyboard these are printed in the same color as the 2 key 8 diamond Activates keys that select certain applications menu items and other operations from the keyboard On the keyboard these are printed in the same color as the 8 key shift Types an uppercase character for the next letter key you press is also used with B and A to highlight c...

Page 142: ... the display If you press a modifier by accident press it again or press N to cancel its effect Other Important Keys You Need to Be Familiar With Key Description 8 Displays the Y Editor 8 Displays the Window Editor 8 Displays the Graph screen 8 Sets parameters for the Table screen ESC QUIT PASTE N accesses the key s primary function 2 K accesses QUIT which is the same color as the 2 key 8 7 access...

Page 143: ...nd off 2 Converts measurement units 8 Designates a measurement unit 0 Deletes the character to the left of the cursor backspaces 2 Toggles between insert and overtype mode for entering information 8 Deletes the character to the right of the cursor Í Enters the with operator which is used in symbolic calculations 2 2 Performs integrations and derivatives 2 Designates an angle in polar cylindrical a...

Page 144: ... algebraic expressions So that you can type them quickly these letters are primary keys on the TI 89 Titanium keyboard 2 Displays the MEMORY screen 2 Displays the VAR LINK screen for managing variables and Flash applications 2 Recalls the contents of a variable 2 9 Displays the UNITS dialog box 2 Displays the CHAR menu which lets you select Greek letters international accented characters etc 2 2 R...

Page 145: ... lowercase alpha character j and then the letter key status line shows Type a single uppercase alpha character and then the letter key status line shows Type a space j alpha function of the key Turn on lowercase alpha lock 2 status line shows Turn on uppercase ALPHA lock status line shows Turn off alpha lock j turns off upper and lowercase lock 2 È types which is the same color as the 2 key j A di...

Page 146: ... you type the character alpha lock remains on Automatic Alpha Lock in TI 89 Titanium Dialog Boxes There are certain times when you do not need to press j or 2 to type alphabetic characters on the TI 89 Titanium Automatic alpha lock is turned on whenever a dialog box is first displayed The automatic alpha lock feature applies to these dialog boxes Dialog box Alpha lock Catalog dialog box All comman...

Page 147: ...lect from a variety of special characters For more information refer to Entering Special Characters in the Text Editor module Entering Numbers The keypad lets you enter positive and negative numbers for your calculations You can also enter numbers in scientific notation Entering a Negative Number 1 Press the negation key Do not use the subtraction key 2 Type the number To see how your graphing cal...

Page 148: ...displays an error message 6 2 4 but 6 2 M12 since it is interpreted as 6 M2 implied multiplication 2 4 2 but 2 4 subtracts 2 from the previous answer and then adds 4 Important Use for subtraction and use for negation Entering a Number in Scientific Notation 1 Type the part of the number that precedes the exponent This value can be an expression Use c and d to include parentheses if you have any do...

Page 149: ...answers to be displayed in scientific or engineering notation Entering Expressions and Instructions You perform a calculation by evaluating an expression You initiate an action by executing the appropriate instruction Expressions are calculated and results are displayed according to the mode settings The display format is determined by the mode settings and the magnitude of the number Represents 1...

Page 150: ...red to enter a value you can enter an expression Operator Performs an operation such as ù Operators require an argument before and after the operator For example 4 5 and 5 2 Function Returns a value Functions require one or more arguments enclosed in parentheses after the function For example 5 and min 5 8 Instruction Initiates an action Instructions cannot be used in expressions Some instructions...

Page 151: ...EOS hierarchy described in the Technical Reference module To change the order of evaluation or just to ensure that an expression is evaluated in the order you require use parentheses Calculations inside a pair of parentheses are completed first For example in 4 1 2 EOS first evaluates 1 2 and then multiplies the answer by 4 If you enter The calculator interprets it as Valid 2p 4 sin 46 5 1 2 or 1 ...

Page 152: ...le For example press 2 W or Select it from a menu if available For example select 2 abs from the Number submenu of the MATH menu or Type the name letter by letter from the keyboard On the TI 89 Titanium use j and 2 to type letters You can use any mixture of uppercase or lowercase letters For example type sin or Sin Example Calculate 3 76 M7 9 5 2 log 45 Type the function name in this example ...

Page 153: ...an also select log by using Press Display 3 76 e c 7 9 2 5 d d 2 2 LOG j c 45 d 3 76 M7 9 2 inserts because its argument must be in parentheses 3 76 M7 9 5 Use d once to close 5 and again to close M7 9 5 3 76 M7 9 5 2log 45 log requires around its argument ...

Page 154: ...ext line To view the entire entry or answer 1 Press C to move the cursor from the entry line up into the history area This highlights the last answer To enter more than one expression or instruction at a time separate them with a colon by pressing 2 Ë Ê Displays last result only Ë is displayed when you press to store a value to a variable If an entry or answer is too long to fit on one line 8 is d...

Page 155: ...ession on the entry line and highlights it You can continue to use the last answer or enter a new expression Example Calculate 3 76 M7 9 5 Then add 2 log 45 to the result 3 Use B and A or 2 B and 2 A to scroll right and left Note When you scroll to the right 7 is displayed at the beginning of the line If you press The calculator p e Z or Replaces the entry line with the variable ans 1 which lets y...

Page 156: ...ated and displayed in any of several formats This section describes the modes and their settings that affect the display formats You can check or change your current mode settings Press Display 3 76 e c 7 9 2 5 d d 2 2 LOG j c 45 d There may be a delay before the Break message is displayed Press N to return to the current application When you press the entry line is replaced with the variable ans ...

Page 157: ...on The entry line does not show an expression in pretty print If pretty print is turned on the history area will show both the entry and its result in pretty print after you press Exact Approx Mode By default Exact Approx AUTO You can use 3 to select from three settings Pretty Print ON OFF p2 p 2 p 2 x 3 2 Because AUTO is a combination of the other two settings you should be familiar with all thre...

Page 158: ...nd symbolic forms EXACT reduces rounding errors that could be introduced by intermediate results in chained calculations 2 Shows whole number results Shows simplified fractional results Shows symbolic p Shows symbolic form of roots that cannot be evaluated to a whole number Press 8 to temporarily override the EXACT setting and display a floating point result ...

Page 159: ... be evaluated they are treated algebraically For example if the variable r is undefined pr2 3 14159 r2 AUTO Uses the EXACT form where possible but uses the APPROXIMATE form when your entry contains a decimal point Also certain functions may display APPROXIMATE results even if your entry does not contain a decimal point Fractional results are evaluated numerically Symbolic forms where possible are ...

Page 160: ...setting press 8 Display Digits Mode By default Display Digits FLOAT 6 which means that results are rounded to a maximum of six digits You can use 3 to select different settings The settings apply to all exponential formats Entry Exact Result Approximate Result Auto Result 8 4 2 2 2 8 6 4 3 1 33333 4 3 8 5ù3 51 2 25 5 25 5 A decimal in the entry forces a floating point result in AUTO 2 2 707107 pù2...

Page 161: ...ation if its magnitude cannot be displayed in the selected number of digits Exponential Format Mode Setting Example Description FIX 0 12 123 123 5 123 46 123 457 FIX 0 FIX 1 FIX 2 FIX 3 Results are rounded to the selected number of decimal places FLOAT 123 456789012 Number of decimal places varies depending on the result FLOAT 1 12 1 E 2 1 2E 2 123 123 5 123 46 123 457 FLOAT 1 FLOAT 2 FLOAT 3 FLOA...

Page 162: ... Editing an Expression in the Entry Line Knowing how to edit an entry can be a real time saver If you make an error while typing an expression it s often easier to correct the mistake than to retype the entire expression Setting Example Description NORMAL 12345 6 If a result cannot be displayed in the number of digits specified by the Display Digits mode the calculator switches from NORMAL to SCIE...

Page 163: ...ve the cursor to the applicable position within the expression Note If you accidentally press C instead of A or B the cursor moves up into the history area Press N or press D until the cursor returns to the entry line To remove the highlight move the cursor toward the side of the expression you want to edit A moves the cursor to the beginning B moves the cursor to the end of the expression To move...

Page 164: ...ng or end of the entry line The first press deletes all characters to the right of the cursor and the second clears the entry line To delete Press The character to the left of the cursor 0 Hold 0 to delete multiple characters The character to the right of the cursor 8 0 All characters to the right of the cursor M once only If there are no characters to the right of the cursor M erases the entire e...

Page 165: ... and overtype modes press 2 Note Look at the cursor to see if you re in insert or overtype mode Replacing or Deleting Multiple Characters First highlight the applicable characters Then replace or delete all the highlighted characters If in The next character you type Will be inserted at the cursor Will replace the highlighted character Thin cursor between characters Cursor highlights a character ...

Page 166: ...w of how to select an item from any menu Specific menus 1 Move the cursor to either side of the characters you want to highlight 2 Hold and press A or B to highlight characters left or right of the cursor 1 Type the new characters 2 Press 0 Note When you highlight characters to replace remember that some function keys automatically add an open parenthesis To replace sin with cos place the cursor b...

Page 167: ...rs Greek math etc 2 I MATH menu Lets you select from categories of math operations CATALOG menu Lets you select from a complete alphabetic list of built in functions and instructions Also lets you select user defined functions or Flash application functions if any have been defined or loaded 2 CUSTOM menu Lets you access a menu that you can customize to list any available function instruction or c...

Page 168: ...pad D and C to highlight the item and then press Note that pressing C from the first item moves the highlight to the last item and vice versa Items Ending with 8 Submenus If you select a menu item ending with 8 a submenu is displayed You then select an item from the submenu 6 indicates that a menu will drop down from the toolbar when you press To select factor press 2 or D This closes the menu and...

Page 169: ...making a selection press A This is the same as pressing N To wrap to the last menu item directly from the first menu item press C To wrap to the first menu item directly from the last menu item press D Because of limited screen size the TI 89 Titanium overlaps these menus indicates that you can use the cursor pad to scroll down for additional items For example List displays a submenu that lets you...

Page 170: ...making a selection press N Depending on whether any submenus are displayed you may need to press N several times to cancel all displayed menus Moving from One Toolbar Menu to Another To move from one toolbar menu to another without making a selection either For example Save Copy As displays a dialog box that prompts you to select a folder name and type a variable name indicates that you can press ...

Page 171: ...plays that item s submenu instead of moving to the next toolbar menu Example Selecting a Menu Item Round the value of p to three decimal places Starting from a clear entry line on the Home screen 1 Press 2 I to display the MATH menu 2 Press 1 to display the Number submenu Or press since the first item is automatically highlighted 3 Press 3 to select round Or press D D and 4 Press 2 T b 3 d and the...

Page 172: ...u 1 If the Apps desktop is off press O to display a menu that lists the applications Note To cancel the menu without making a selection press N 2 Select an application Either Use the cursor pad D or C to highlight the application and then press or Press the number or letter for that application Application Lets you FlashApps Display a list of Flash applications if any Y Editor Define edit and sele...

Page 173: ...le values that correspond to an entered function Data Matrix Editor Enter and edit lists data and matrices You can perform statistical calculations and graph statistical plots Program Editor Enter and edit programs and functions Text Editor Enter and edit a text session Numeric Solver Enter an expression or equation define values for all but one variable and then solve for the unknown variable Hom...

Page 174: ... an application Press O In full screen mode press 2 K In split screen mode press 2 K to open the full screen view of the active application then press 2 K again To return to the last open application from the Apps desktop press 2 a Option Description Current Returns the screen displayed when you last viewed the App If there is no current file variable for the selected App this option defaults to N...

Page 175: ...Operating the Calculator 172 From the Keyboard ...

Page 176: ...re displayed and interpreted Mode settings are retained by the Constant Memory feature when the graphing calculator is turned off All numbers including elements of matrices and lists are displayed according to the current mode settings Checking Mode Settings Press 3 to display the MODE dialog box which lists the modes and their current settings Application Press Home Y Editor 8 Window Editor 8 Gra...

Page 177: ...id are dimmed For example on Page 2 Split 2 App is not valid when Split Screen FULL When you scroll through the list the cursor skips dimmed settings Changing Mode Settings From the MODE dialog box 1 Highlight the mode setting you want to change Use D or C with ƒ or to scroll through the list 2 Press B or A to display a menu that lists the valid settings The current setting is highlighted 3 Select...

Page 178: ...de look in the applicable section of this guidebook Mode Description Graph Type of graphs to plot FUNCTION PARAMETRIC POLAR SEQUENCE 3D or DE Current Folder Folder used to store and recall variables Unless you have created additional folders only the MAIN folder is available Refer to Using Folders to Store Independent Sets of Variables in Calculator Home Screen Display Digits Maximum number of dig...

Page 179: ...efer to the Split Screens module Split 1 App Application in the top or left side of a split screen If you are not using a split screen this is the current application Split 2 App Application in the bottom or right side of a split screen This is active only for a split screen Number of Graphs For a split screen lets you set up both sides of the screen to display independent sets of graphs Graph 2 I...

Page 180: ... of measurement to specify the default units for displayed results SI metric or MKS Eng US feet pounds etc or Custom Custom Units Lets you select custom defaults The mode is dimmed until you select Unit System 3 CUSTOM Language Lets you localize the calculator into one of several languages depending on which language Flash applications are installed Apps Desktop Turns the Apps desktop ON or OFF To...

Page 181: ...eginning the calculation NewProb Places NewProb in the entry line You must then press to execute the command NewProb performs a variety of operations that let you begin a new problem from a cleared state without resetting the memory Clears all single character variable names in the current folder same as 1 Clear a z unless the variables are locked or archived Turns off all functions and stat plots...

Page 182: ...Management Using the Catalog Dialog Box The CATALOG provides a way to access any built in command functions and instructions from one convenient list In addition the CATALOG dialog box lets you select functions used in Flash applications or user defined functions if any have been loaded or defined Displaying the CATALOG To display the CATALOG dialog box press The CATALOG defaults to Built in which...

Page 183: ...on or a program Selecting a Built in Command from the CATALOG When you select a command its name is inserted in the entry line at the cursor location Therefore you should position the cursor as necessary before selecting the command 1 Press 2 Press Built in Note The first time you display the Built in list it starts at the top of the list The next time you display the list it starts at the same pl...

Page 184: ...us line shows the required and optional parameters if any and their type Ê Indicated command and its parameters Ë Brackets indicate optional parameters To move the 8 indicator Press or type One function or program at a time D or C One page at a time 2 D or 2 C To the first function that begins with a specified letter The letter key On the TI 89 Titanium do not press j first If you do you need to p...

Page 185: ...eters in a dialog box by pressing ƒ Help The parameters are the same as those displayed on the status line Some commands such as ClrDraw do not require parameters If you select one of these commands parameters will not display on the status line and you will see Unavailable if you press ƒ Help Press N to exit the CATALOG Help dialog box factor expression or factor expression variable required opti...

Page 186: ...e the 8 indicator to the function and press The list is alphabetized by function name The left column lists functions The right column lists the Flash application that contains the function Information about a function is displayed in the status line To exit without selecting a function press N To move the 8 indicator Press or type One function or program at a time D or C One page at a time 2 D or...

Page 187: ...ry line at the cursor location Therefore you should position the cursor as necessary before selecting the function or program 1 Press 2 Press User Defined This option is dimmed if you have not defined a function or created a program Note Use the VAR LINK screen to manage variables folders and Flash applications See the Memory and Variable Management module The list is alphabetized by function prog...

Page 188: ...o 8 characters consisting of letters and digits This includes Greek letters but not p accented letters and international letters Do not include spaces The first character cannot be a digit Can use uppercase or lowercase letters The names AB22 Ab22 aB22 and ab22 all refer to the same variable To move the 8 indicator Press or type One function or program at a time D or C One page at a time 2 D or 2 ...

Page 189: ... module System variables such as xmin and xmax which are used to store graph related values Refer to the Technical Reference module for a list Examples Data Types Variable Description myvar OK a OK Log Not OK name is preassigned to the log function Log1 OK 3rdTotal Not OK starts with a digit circumfer Not OK more than 8 characters DataTypes Examples Expressions 2 54 1 25E6 2p xmin 10 2 3i x 2 2 Li...

Page 190: ...riable temporarily you can use the with operator Refer to Substituting Values and Setting Constraints in Symbolic Manipulation Matrices Character strings Hello The answer is xmin 10 Pictures Functions myfunc arg ellipse x y r1 r2 3 Type the variable name Note TI 89 Titanium users should use j as necessary when typing variable names 4 Press DataTypes Examples 1 0 0 1 0 0 3 4 6 ...

Page 191: ...d Therefore it is used as a symbolic variable Note Refer to Symbolic Manipulation for information about symbolic manipulation 1 Type the variable name into the expression 2 Press to evaluate the expression Note To view a list of existing variable names use 2 as described in Memory and Variable Management If you want the result to replace the variable s previous value you must store the result The ...

Page 192: ...serted at the cursor position in the entry line Status Line Indicators in the Display The status line is displayed at the bottom of all application screens It shows information about the current state of the calculator including several important mode settings Status Line Indicators Ê Current Folder Ë Modifier Key Ì Angle Mode 1 Press 2 to display a dialog box 2 Type the variable name 3 Press twic...

Page 193: ...below 2nd 2 will use the second function of the next key you press 2 8 will use the diamond feature of the next key you press will type the uppercase letter for the next key you press On the TI 89 Titanium you can use to type a letter without having to use j j will type the lowercase letter for the next key you press 2 lowercase alpha lock is on Until you turn this off will type the lowercase lett...

Page 194: ...te Graph Number If the screen is split to show two independent graphs this indicates which graph is active G1 or G2 Graph Mode Indicates the type of graphs that can be plotted To change the Graph mode use the 3 key FUNC y x functions PAR x t and y t parametric equations POL r q polar equations SEQ u n sequences 3D z x y 3D equations DE y t differential equations Battery Displayed only when the bat...

Page 195: ... in this part of the status line depends on the application you are using 23 30 Displayed on the Home screen to show the number of entry answer pairs in the history area Refer to History Information on the Status Line in the Calculator Home Screen module BUSY A calculation or graph is in progress PAUSE You paused a graph or program Œ The variable opened in the current editor Data Matrix Editor Pro...

Page 196: ...nd paste and more Note The term calculator Home screen is used in this module Other modules use the term Home screen Both terms are interchangeable and refer to the same screen Displaying the Calculator Home Screen When you first turn on your TI 89 Titanium the Apps desktop is displayed To display the calculator Home screen highlight the Home icon and press You can also display the calculator Home...

Page 197: ...n the same form in which they are written on the board or in textbooks Ê Toolbar Lets you display menus for selecting operations applicable to the calculator Home screen To display a toolbar menu press ƒ etc Ë Pretty Print Display Shows exponents roots fractions etc in traditional form Ì Last Entry Your last entry Í Entry Line Where you enter expressions or instructions Î Status Line Shows the cur...

Page 198: ...tes the entry is longer than the screen width Ê Last Entry Pretty print is ON Exponents roots fractions etc are displayed in the same form in which they are traditionally written Ë History Area Lists entry answer pairs you have entered Pairs scroll up the screen as you make new entries Ì Answer Continues Highlight the answer and press B to scroll right and view the rest of it Note that the answer ...

Page 199: ... can re use or edit it Scrolling through the History Area Normally the cursor is in the entry line However you can move the cursor into the history area To Do this View entries or answers that have scrolled off the screen From the entry line press C to highlight the last answer Continue using C to move the cursor from answer to entry up through the history area Go to the oldest or newest history p...

Page 200: ...u make a new entry indicated by 30 30 the new entry answer pair is saved and the oldest pair is deleted The history indicator does not change Return the cursor to the entry line Press N or press D until the cursor is back on the entry line To Do this 8 30 If the cursor is on the entry line If the cursor is in the history area Maximum number of pairs that can be saved Total number of pairs that are...

Page 201: ... as a command script Saving the Entries in the History Area To Do this Change the number of pairs that can be saved Press ƒ and select 9 Format or press 8 Í Then press B use C or D to highlight the new number and press twice Clear the history area and delete all saved pairs Press ƒ and select 8 Clear Home or enter ClrHome on the entry line Delete a particular entry answer pair Move the cursor to e...

Page 202: ...tor Home screen On the calculator Home screen s ƒ toolbar menu 1 Open is not available Instead 2 Specify a folder and text variable that you want to use to store the entries Note Only the entries are saved not the answers Item Description Type Automatically set as Text and cannot be changed Folder Shows the folder in which the text variable will be stored To use a different folder press B to displ...

Page 203: ...command script refer to the Text Editor module Cutting Copying and Pasting Information Cut copy and paste operations let you move or copy information within the same application or between different applications These operations use the clipboard which is an area in memory that serves as a temporary storage location Auto paste vs Cut Copy Paste Auto paste is a quick way to copy an entry or answer ...

Page 204: ...tting or Copying Information to the Clipboard When you cut or copy information that information is placed in the clipboard However cutting deletes the information from its current location used to move information and copying leaves the information 1 Highlight the characters that you want to cut or copy In the entry line move the cursor to either side of the characters Hold and press A or B to hig...

Page 205: ...you cut or copy information it replaces the clipboard s previous contents if any Pasting Information from the Clipboard A paste operation inserts the contents of the clipboard at the current cursor location on the entry line This does not change the contents of the clipboard 1 Position the cursor where you want to paste the information Clipboard empty or the previous contents After cut After copy ...

Page 206: ...ant to reuse an expression without retyping it each time 1 Copy the applicable information 2 Paste the copied information into a new entry a Begin a new entry and place the cursor where you want to paste the copied information a Use B or A to highlight the expression b Press 8 6 c For this example press to evaluate the entry ...

Page 207: ...on 3 Paste the copied information into a different application Note By copying and pasting you can easily transfer information from one application to another c Press 8 7 to paste the copied expression d Complete the new entry and press a Press 8 to display the Y Editor b Press to define y1 x c Press 8 7 to paste d Press to save the new definition ...

Page 208: ...he Expression on the Entry Line When you press to evaluate an expression the TI 89 Titanium leaves that expression on the entry line and highlights it You can type over the entry or you can reuse it as necessary For example using a variable find the square of 1 2 3 etc As shown below set the initial variable value and then enter the variable expression Next reenter to increment the variable and ca...

Page 209: ... that covers 200 square centimeters Note Editing an entry lets you make minor changes without retyping the entire entry The example below uses 8 as the first guess and then displays the answer in its approximate floating point form You can edit and reexecute using 7 95 and continue until the answer is as accurate as you want TI 89 Titanium Display 8 j R 2 Ë 2 T j R Z 2 8 TI 89 Titanium Display ...

Page 210: ... is currently shown on the entry line You can then reexecute or edit the recalled entry Note You can also use the entry function to recall any previous entry Refer to entry in the Technical Reference module For example A 8 8 7 95 To recall Press Effect The last entry if you ve changed the entry line 2 once If the last entry is still shown on the entry line this recalls the entry prior to that Prev...

Page 211: ...eld per square meter if the plot produces a total of 147 tomatoes Just as ans 1 always contains the last answer ans 2 ans 3 etc also contain previous answers For example ans 2 contains the next to last answer Note Refer to ans in the Technical Reference module 1 Find the area 1 7 p 4 2 2 Find the yield 147 e 2 If the entry line contains the last entry 2 recalls this entry If the entry line is edit...

Page 212: ...uto paste is similar to 2 and 2 as described in the previous section but there are differences Note You can also paste information by using the ƒ toolbar menu For entries Pasting lets you 2 lets you Insert any previous entry into the entry line Replace the contents of the entry line with any previous entry For answers Pasting lets you 2 lets you Insert the displayed value of any previous answer in...

Page 213: ...is pastes the entire entry or answer If you need only a part of the entry or answer edit the entry line to delete the unwanted parts C moves from answer to entry up through the history area You can use C to highlight items that have scrolled off the screen Note To cancel auto paste and return to the entry line press N To view an entry or answer too long for one line indicated by 8 at the end of th...

Page 214: ...many arguments as necessary In these examples the definition consists of a single expression or statement When defining functions and programs use unique names for arguments that will not be used in the arguments for a subsequent function or program call Note Function names follow the same rules as variable names Refer to Storing and Recalling Variable Values in Operating the Calculator In the arg...

Page 215: ...pecifically pass x and y as the arguments when you evaluate the function Creating a User Defined Function Use one of the following methods Method Description Store an expression to a function name including the argument list Define command Define a function name including the argument list as an expression Program Editor Refer to Programming or information on creating a user defined function ...

Page 216: ...unctions and programs refer to Programming For example suppose you want to create a function that sums a series of reciprocals based on an entered integer n When creating the definition of a multi statement function it may be helpful to visualize it first in a block form Ê Func and EndFunc must begin and end the function Ë Variables not in the argument list must be declared as local Ê Ë Ì Í Î Ê Fu...

Page 217: ... would for a single statement function Note It s easier to create a complicated multi statement function in the Program Editor than on the calculator Home screen Refer to Programming On the calculator Home screen Define sumrecip nn Func Local temp i EndFunc Use a colon to separate each statement Use argument names that will never be used when calling the function or program Multi statement functio...

Page 218: ...ny other function Evaluate it by itself or include it in another expression To Do this Display a list of all user defined functions Press 2 to display the VAR LINK screen You may need to use the View toolbar menu to specify the Function variable type Refer to Memory and Variable Management or Press Display a list of Flash application functions Press ...

Page 219: ... free memory Display the definition of a user defined function From the VAR LINK screen highlight the function and display the Contents menu 2 ˆ or From the calculator Home screen press 2 Type the function name but not the argument list such as xroot and press twice or From the Program Editor open the function Refer to Programming Edit the definition From the calculator Home screen use 2 to displa...

Page 220: ... answer that is both too long and too tall to be displayed on the screen Note This example uses the randMat function to generate a 25 x 25 matrix If There Is not Enough Memory A symbol is displayed when the TI 89 Titanium does not have enough free memory to display the answer Press B or 2 B to scroll right Press A or 2 A to scroll left Ê Ë Ì Í Ê Press C or C to scroll up Ë Press D to scroll down Ì...

Page 221: ...you can try to Free up additional memory by deleting unneeded variables and or Flash applications Use 2 as described in Memory and Variable Management If possible break the problem into smaller parts that can be calculated and displayed with less memory Using the Custom Menu The TI 89 Titanium has a custom menu that you can turn on and off at any time You can use the default custom menu or create ...

Page 222: ...e the custom menu on and off Note You can also turn the custom menu on and off by entering CustmOn or CustmOff in the entry line and pressing Unless the menu has been modified the default custom menu appears Menu Function ƒ Var Common variable names f x Function names such as f x g x and f x y Solve Items related to solving equations Unit Common units such as _m _ft and _l Symbol Symbols such as a...

Page 223: ... 2 to turn off the custom menu and display the calculator Home screen s normal toolbar menu This pastes the commands used to create the default menu into the entry line Note The previous custom menu is erased If that menu was created with a program it can be recreated later by running the program again 3 Press to execute the commands and restore the default International 2 ˆ Commonly accented char...

Page 224: ...ions such as If you obtain new or upgraded software or Flash applications for your TI 89 Titanium you may need to provide your current software version and or the ID number of your unit If you have difficulties with your TI 89 Titanium and need to contact technical support knowing the software version may make it easier to diagnose the problem 1 From either the calculator Home screen or the Apps d...

Page 225: ...athematics Software version Product identifier Product ID Unit ID Apps certificate revision number Cert Rev Ê OS version Ë Product identifier Ì Apps certificate revision number Í Hardware version Î Unit ID required to obtain certificates for installing purchased Apps Your screen will be different from the one shown above Ê Ë Ì Í Î ...

Page 226: ...ssion that you anticipated How Undefined and Defined Variables Are Treated When you enter an expression that contains a variable the TI 89 Titanium treats the variable in one of two ways To see why this is important suppose you want to find the first derivative of x3 with respect to x If the variable is undefined it is treated as an algebraic symbol If the variable is defined even if defined as 0 ...

Page 227: ... character in the name Leave one character names undefined for symbolic calculations Method Example Enter the variable name Use the getType function Unless you knew that 5 had been stored to x previously the answer 75 could be misleading If defined the variable s value is displayed If undefined the variable name is displayed If defined the variable s type is displayed If undefined NONE is displaye...

Page 228: ... Do this One or more specified variables Use the DelVar function You can also delete variables by using the VAR LINK screen 2 as described in Memory and Variable Management All one letter variables a z in the current folder Note For information about folders refer to the Calculator Home Screen module From the Home screen Clean Up menu select 1 Clear a z You will be prompted to press to confirm the...

Page 229: ...scribed briefly in Operating the Handheld directly affect the precision and accuracy with which the TI 89 Titanium calculates a result This section describes these mode settings as they relate to symbolic manipulation EXACT Setting When Exact Approx EXACT the handheld uses exact rational arithmetic with up to 614 digits in the numerator and 614 digits in the denominator The EXACT setting Temporari...

Page 230: ...ing Some equations such as 2Lx x have solutions that cannot all be finitely represented in terms of the functions and operators on the handheld With this kind of equation EXACT will not compute approximate solutions For example 2Lx x has an approximate solution x 0 641186 but it is not displayed in the EXACT setting Advantages Disadvantages Results are exact As you use more complicated rational nu...

Page 231: ...2 0 transforms to x2 even in the APPROXIMATE setting Functions such as solve and integrate can use both exact symbolic and approximate numeric techniques These functions skip all or some of their exact symbolic techniques in the APPROXIMATE setting Advantages Disadvantages If exact results are not needed this might save time and or use less memory than the EXACT setting Approximate results are som...

Page 232: ... leap over barriers such as undefined variables or between elements of lists or matrices For example 1 2 1 3 x 0 5 1 3 y transforms to x 6 16666666666667 y and 1 2 1 3 0 5 1 3 transforms to 1 6 16666666666667 If you do not plan to use symbolic computations approximate results are similar to familiar traditional numeric calculators Symbolic operations such as limits and integration are less likely ...

Page 233: ...tanium automatically simplifies the expression according to its default simplification rules Advantages Disadvantages You see exact results when practical and approximate numeric results when exact results are impractical You can often control the format of a result by choosing to enter some coefficients as either rational or floating point numbers If you are interested only in exact results some ...

Page 234: ...or functions The arguments are simplified Some built in functions delay simplification of some of their arguments If the function is a built in or user defined function the function definition is applied to the simplified arguments Then the functional form is replaced with this result If a variable has a defined value that value replaces the variable If the variable is defined in terms of another ...

Page 235: ...nstants and are placed in alphabetical order at the end of a sum but before numbers Similar factors and similar terms are collected Identities involving zeros and ones are exploited Polynomial greatest common divisors are canceled Polynomials are expanded unless no key cancellation can occur This floating point number causes numeric results to be shown as floating point If a floating point whole n...

Page 236: ...tion of the expression Auto paste the entire expression on the entry line and then delete the unwanted parts Delayed Simplification for Certain Built In Functions Usually variables are automatically simplified to their lowest possible level before they are passed to a function For certain functions however complete simplification is delayed until after the function is performed Common denominators...

Page 237: ...r argument use delayed simplification For a function that uses delayed simplification 1 The var variable is simplified to the lowest level at which it remains a variable even if it could be further simplified to a non variable value 2 The function is performed using the variable 3 If var can be further simplified that value is then substituted into the result Note You may or may not want to define...

Page 238: ...nstraints Note The example to the right finds the derivative of x3 at x 5 If x3 was initially simplified to 75 you would find the derivative of 75 which is not what you want x cannot be simplified x is not simplified The function uses x3 and then substitutes 5 for x x is simplified to t The function uses t3 x is simplified to t The function uses t3 and then substitutes 5 for t ...

Page 239: ...he with operator press Í Substituting for a Variable For every occurrence of a specified variable you can substitute a numeric value or an expression To substitute for multiple variables at the same time use the Boolean and operator First derivative of x3 at x 5 ...

Page 240: ...able You can also use z_ For more information see the _ underscore topic in the Technical Reference module For every occurrence of a simple expression you can substitute a variable numeric value or another expression By replacing a commonly used or long term you can display results in a more compact form Note acos x is different from a cos x You can substitute complex values just as you would for ...

Page 241: ...ule To get the complex i press 2 Do not simply type the letter i on the keyboard Be Aware of the Limitations of Substitutions Substitution occurs only where there is an exact match for the substitution Only x2 was replaced not x4 Define the substitution in simpler terms for a more complete substitution ...

Page 242: ...cursion Internally an expression is sorted according to the automatic simplification rules Therefore products and sums may not match the order in which you entered them An error message is displayed When you press N an error is shown in the history area As a general rule you should substitute for a single variable sin x x x 1 Substitutes sin x 1 sin x 1 1 sin x 1 1 1 etc ...

Page 243: ...ral expressions either møc2 e or c2 øm e may not work as you anticipate Note Use the solve function to help determine the single variable substitution ln x y ln x ln y only if x and or y is not negative Sin 1 sin q q only if q Lp 2 and q p 2 radians Because ln x y ln x ln y is not always valid the logarithms are not combined With a constraint the identity is valid and the expression is simplified ...

Page 244: ...ariable However substitution is preferable for most cases because the variable is defined only for the current calculation and does not accidentally affect later calculations Because sinL1 sin q q is not always valid the expression is not simplified With a constraint the expression can be simplified In many cases you can achieve the same effect as a substitution by defining the variable Substituti...

Page 245: ...x Overview of the Algebra Menu You can use the Algebra toolbar menu to select the most commonly used algebraic functions The Algebra Menu From the Home screen press to display Storing 1 x affects the subsequent calculations calculation This menu is also available from the MATH menu Press 2 I and then select 9 Algebra ...

Page 246: ...espect to all its variables or with respect to only a specified variable zeros Determines the values of a specified variable that make an expression equal to zero Displays in a list approx Evaluates an expression using floating point arithmetic where possible This is equivalent to using 3 to set Exact Approx APPROXIMATE or using 8 to evaluate an expression comDenom Calculates a common denominator ...

Page 247: ...multiple angles tCollect is the opposite of tExpand Complex Displays the submenu These are the same as solve factor and zeros but they also compute complex results Extract Displays the submenu getNum Applies comDenom and then returns the resulting numerator getDenom Applies comDenom and then returns the resulting denominator left Returns the left hand side of an equation or inequality Menu Item De...

Page 248: ...ection gives examples for some of the functions available from the Algebra toolbar menu For complete information about any function refer to the Technical Reference module Some algebraic operations do not require a special function Adding or Dividing Polynomials right Returns the right hand side of an equation or inequality You can add or divide polynomials directly without using a special functio...

Page 249: ...do more than simply factor an algebraic polynomial Factor x5 N 1 Then expand the result Notice that factor and expand perform opposite operations You can find prime factors of a rational number either an integer or a ratio of integers factor expression var for factoring with respect to a variable expand expression var for partial expansion with respect to a variable ...

Page 250: ...t collects similar powers of a variable Solving an Equation Use the solve 1 function to solve an equation for a specified variable solve equation var Do a full expansion of x2 Nx y2 Ny with respect to all variables Then do a partial expansion with respect to x Solve x y N 5 2x N 5y for x Notice that solve displays only the final result ...

Page 251: ...er a set of two equations with two unknowns 2x N 3y 4 Lx 7y L12 Method Example Use the solve function for a one step solution solve 2xN3y 4 and Lx 7y L12 x y Use the solve function with substitution for step by step manipulation Substitutions are in the form of an equality such as x 3 or y sin x To be most effective the left side should be a simple variable See Symbolic Manipulation in the Preview...

Page 252: ...s are not on the Algebra menu Use 2 I 4 or the Catalog Use the simult function with a matrix Enter the coefficients as a matrix and the results as a constant column matrix Use the rref function with a matrix Enter the coefficients as an augmented matrix Method Example ...

Page 253: ...he zeros 4 function zeros expression var Use the expression x sin x cos x Find the zeros with respect to x in the interval 0 x and x 3 Note For or type 8 Ã or 8 Â You can also use 2 I 8 or 2 G 2 to select them from a menu Use the with operator to specify the interval ...

Page 254: ...y expanded numerator and a fully expanded denominator Notice that propFrac and comDenom perform opposite operations Note You can use comDenom with an expression list or matrix propFrac rational expression var for proper fractions with respect to a variable comDenom expression var for common denominators that collect similar powers of this variable If you do this example on your handheld the propFr...

Page 255: ...lus functions The Calc Menu From the Home screen press to display Note For a complete description of each function and its syntax refer to the Technical Reference module This menu is also available from the MATH menu Press 2 I and then select A Calculus Menu Item Description d differentiate Differentiates an expression with respect to a specified variable 31x 60 8 x 2 2 x 4 15 8 ...

Page 256: ...tes the product fMin Finds candidate values of a specified variable that minimize an expression fMax Finds candidate values of a specified variable that maximize an expression arcLen Returns the arc length of an expression with respect to a specified variable taylor Calculates a Taylor polynomial approximation to an expression with respect to a specified variable nDeriv Calculates the numerical de...

Page 257: ... module Integrating and Differentiating Use the integrate 2 and d differentiate 1 functions d expression var order Note You can integrate an expression only you can differentiate an expression list or matrix Integrate x2 sin x with respect to x Differentiate the answer with respect to x expression var low up lets you specify limits or a constant of integration To get d use 1 or 2 Do not simply typ...

Page 258: ...Use the limit 3 function Note You can find a limit for an expression list or matrix Find the limit of sin 3x x as x approaches 0 limit expression var point direction negative number from left positive number from right omitted number or 0 both ...

Page 259: ... Functions and Symbolic Manipulation You can use a user defined function as an argument for the TI 89 Titanium s built in algebra and calculus functions Find a 6th order Taylor polynomial for sin x with respect to x Store the answer as a user defined function named y1 x Then graph sin x and the Taylor polynomial taylor expression var order point if omitted expansion point is 0 Graph sin x Graph y1...

Page 260: ...of Entering a Function in the Programming module Undefined Functions You can use functions such as f x g t r q etc that have not been assigned a definition These undefined functions yield symbolic results For example Single Statement Functions You can use user defined functions consisting of a single expression For example Use DelVar to ensure that f x and g x are not defined Then find the derivat...

Page 261: ...tions should be used as an argument for numeric functions such as nDeriv and nInt only Then find the limit of sec x as x approaches p 4 Note To select limit from the Calc toolbar menu press 3 Then find a 5th order Taylor polynomial for h x with respect to x Note To select from the Calc toolbar menu press 2 or press 2 on the keyboard To select taylor press 9 x sec 1 x cos h x t sin t 0 x Define h x...

Page 262: ...ction with two pieces If you were to create a multi statement user defined function with the form Note To select nInt from the Calc toolbar menu press B nInt When Use expression x 0 x 0 Lx 5 cos x Func If x 0 Then Return ëx Else Return 5cos x EndIf EndFunc Then numerically integrate y1 x with respect to x Define y1 x Func If x 0 Then EndFunc ...

Page 263: ...ut of memory before a result can be calculated Freeing Up Memory Delete unneeded variables and or Flash applications particularly large sized ones Use 2 as described in Memory and Variable Management to view and delete variables and or Flash applications On the Home screen Use the TI 89 Titanium s built in when function Then integrate y1 x with respect to x Note To select from the Calc toolbar men...

Page 264: ...d combine the results If several undefined variables occur only in a certain combination replace that combination with a single variable If m and c occur only as m c2 substitute e for m c2 In the expression substitute c for a b and use In the solution replace c with a b For expressions combined over a common denominator replace sums in denominators with unique new undefined variables In the expres...

Page 265: ...cial Constants Used in Symbolic Manipulation The result of a calculation may include one of the special constants described in this section In some cases you may also need to enter a constant as part of your entry true false These indicate the result of an identity or a Boolean expression x x is true for any value of x 5 3 is false ...

Page 266: ...bitrary integer consecutive numbering restarts at n0 Use Clean Up 2 NewProb to reset to n1 Note For press 8 9 ˆ represents infinity and e represents the constant 2 71828 base of the natural logarithms These constants are often used in entries as well as results Notes For ˆ press 8 For e press 8 s A solution is at every integer multiple of p Both n1 and n2 represent any arbitrary integer but this n...

Page 267: ...Symbolic Manipulation 264 undef This indicates that the result is undefined Mathematically undefined ˆ undetermined sign Non unique limit ...

Page 268: ...type them directly from the keyboard From a Menu The following shows how to select a unit but you can use the same general procedure to select a constant From the Home screen 1 Type the value or expression 2 Display the UNITS dialog box Press 2 9 3 Use D and C to move the cursor to the applicable category Note Use 2 D and 2 C to scroll one page at a time through the categories 6 3 ...

Page 269: ...g units to a variable you must put a space or before the underscore For example x_m is treated as a variable not as x with a unit Note You can type units in either uppercase or lowercase characters 4 To select the highlighted default unit press or To select a different unit from the category press B Then highlight the applicable unit and press Note If you created a user defined unit for an existin...

Page 270: ... for frequently used combinations For example suppose you want to enter a velocity in meters per second In the UNITS dialog box however the Velocity category does not contain this unit You can enter meters per second by combining _m and _s from the Length and Time categories respectively 3 9 8_m _s Combine the units _m and _s There is no pre defined m _s unit ...

Page 271: ... will be evaluated group them within parentheses Here s why you get unexpected units if you do not use parentheses In a calculation a unit is treated similar to a variable For example 100_m is treated as 100 _m and 2_s is treated as 2 _s Without parentheses the entry is calculated as 100 _m 2 _s _s 50 _m _s To calculate Enter 100_m 2_s 100_m 2_s 50 _m _s You must use parentheses for 2_s This is im...

Page 272: ...nverted and displayed automatically in the current default unit for that category unless you use the 4 conversion operator as described later The following examples assume that your default units are set to the SI system of metric units Notes Refer to the list of pre defined units From the UNITS dialog box you can select available units from a menu To multiply 20 times 6 kilometers 20 6_km Shown i...

Page 273: ...want to convert to a unit other than the default use the 4 conversion operator To convert 4 light years to kilometers 4_ltyr 4 _km To convert 186000 miles second to kilometers hour 186000_mi _s 4 _km _hr expression_unit1 4 _unit2 For 4 press 2 4 ...

Page 274: ...6000 miles second from miles to kilometers 186000_mi _s 4 _km To convert 186000 miles second from seconds to hours 186000_mi _s 4 1 _hr To enter meters per second squared 27_m _s 2 To convert meters per second squared from seconds to hours 27_m _s 2 4 1 _hr 2 Because a Time conversion is not specified it is shown in its default unit _s in this example Because a Length conversion is not specified i...

Page 275: ...2 For Temperature Values To convert a temperature value you must use tmpCnv instead of the 4 operator For example to convert 100_ C to _ F tmpCnv 100_ c _ f tmpCnv expression_ tempUnit1 _ tempUnit2 For press 2 v 0 100 32 212 _ C _ F o o ...

Page 276: ...ault Units for Displayed Results All results involving units are displayed in the default unit for that category For example if the default unit for Length is _m any length result is displayed in meters even if you entered _km or _ft in the calculation For example to convert a 100_ C range to its equivalent range in _ F tmpCnv 100_ c _ f Note For press 8 c 7 D 0 100 32 212 _ C _ F o o 100_ C o 180...

Page 277: ...reen use built in default units which you cannot change The default units for these systems are available To set custom defaults 1 Press 3 B 3 to set Unit System CUSTOM 2 Press D to highlight SET DEFAULTS 3 Press B to display the CUSTOM UNIT DEFAULTS dialog box If Unit System SI or ENG US the Custom Units item is dimmed You cannot set a default for individual categories ...

Page 278: ...nits What is the NONE Default Many categories let you select NONE as the default unit 4 For each category you can highlight its default press B and select a unit from the list 5 Press twice to save your changes and exit the MODE screen This means that results in that category are displayed in the default units of its components For example Area Length2 so Length is the component of Area You can al...

Page 279: ...hy Use Your Own Units Some example reasons to create a unit are You want to enter length values in dekameters Define 10_m as a new unit named _dm Instead of entering _m _s2 as an acceleration unit you define that combination of units as a single unit named _ms2 You want to calculate how many times someone blinks You can use _blinks as a valid unit without defining it This standalone unit is treate...

Page 280: ... to 8 characters First character must be an underscore For _ press 8 5 Second character can be any valid variable name character except _ or a digit For example _9f is not valid Remaining characters up to 6 can be any valid variable name character except an underscore Defining a Unit Define a unit the same way you store to a variable ...

Page 281: ...re stored as variables You can delete them the same as you would any variable For example to define a dekameter unit 10_m _dm To define an acceleration unit _m _s 2 _ms2 To calculate 195 blinks in 5 minutes as _blinks _min 195_blinks 5_min definition _newUnit For press 9 Assuming unit defaults for Length and Time are set to _m and _s Assuming unit default for Time is set to _s ...

Page 282: ...tems of measurement use built in default units In this section the built in defaults are indicated by SI and ENG US In some categories both systems use the same default Some categories do not have default units Constants Description Value _c speed of light 2 99792458E8_m _s _Cc coulomb constant 8 9875517873682E9_Nø_m2 _coul2 _g acceleration of gravity 9 80665_m _s2 _Gc gravitational constant 6 672...

Page 283: ...proton rest mass 1 6726231E M27_kg _Na Avogadro s number 6 0221367E23 _mol _q electron charge 1 60217733E M19_coul _Rb Bohr radius 5 29177249E M11_m _Rc molar gas constant 8 31451_J _mol _ K _Rdb Rydberg constant 10973731 53413 _m _Vm molar volume 2 241409E M2_m3 _mol _H0 permittivity of a vacuum 8 8541878176204E M12_F _m _s Stefan Boltzmann constant 5 6705119E M8_W _m2 _ K4 _f0 magnetic flux quan...

Page 284: ... _cm centimeter _mm millimeter _fath fathom _Nmi nautical mile _fm fermi _pc parsec _ft foot ENG US _rod rod _in inch _yd yard _km kilometer _m micron _ltyr light year _Å angstrom _m meter SI _acre acre NONE SI ENG US _ha hectare _cup cup _ml milliliter _floz fluid ounce _pt pint _flozUK British fluid ounce _qt quart ...

Page 285: ...p tablespoon _galUK British gallon _tsp teaspoon _l liter NONE SI ENG US _day day _s second SI ENG US _hr hour _week week _min minute _yr year _ms millisecond _ms microsecond _ns nanosecond _knot knot _mph miles per hour _kph kilometers per hour NONE SI ENG US no pre defined units ...

Page 286: ...nce Mass _ C Celsius For press 2 _ K Kelvin _ F Fahrenheit _ R Rankine no default _cd candela no default _mol mole no default _amu atomic mass unit _oz ounce _gm gram _slug slug _kg kilogram SI _ton ton _lb pound ENG US _tonne metric ton _mg milligram _tonUK long ton _mton metric ton ...

Page 287: ...nf ton force _lbf pound force ENG US _Btu British thermal unit ENG US _J joule SI _cal calorie _kcal kilocalorie _erg erg _kWh kilowatt hour _eV electron volt _latm liter atmosphere _ftlb foot pound _hp horsepower ENG US _W watt SI _kW kilowatt _atm atmosphere _mmHg millimeters of mercury _bar bar _Pa pascal SI ...

Page 288: ...rrent _inH2O inches of water _psi pounds per square inch ENG US _inHg inches of mercury _torr millimeters of mercury _mmH2O millimeters of water _St stokes _P poise _GHz gigahertz _kHz kilohertz _Hz hertz SI ENG US _MHz megahertz _A ampere SI ENG US _mA milliampere _kA kiloampere _mA microampere ...

Page 289: ...nce Capacitance _coul coulomb SI ENG US _kV kilovolt _V volt SI ENG US _mV millivolt _volt volt _kJ kilo ohm _ohm ohm _MJ megaohm _J ohm SI ENG US _mho mho ENG US _siemens siemens SI _mmho millimho _mmho micromho _F farad SI ENG US _pF picofarad _nF nanofarad _mF microfarad ...

Page 290: ...rement Units 287 Mag Field Strength Mag Flux Density Magnetic Flux Inductance _Oe oersted NONE SI ENG US _Gs gauss _T tesla SI ENG US _Wb weber SI ENG US _henry henry SI ENG US _nH nanohenry _mH millihenry _mH microhenry ...

Page 291: ... detailed description of each step refer to the following pages You may not need to do all the steps each time you graph a function Graphing Functions 1 Set Graph mode 3 to FUNCTION Also set Angle mode if necessary 2 Define x and y components on Y Editor 8 3 Select which defined functions to graph Note To turn off any stat data plots press 5 or use to deselect them ...

Page 292: ...y tracing a function Use the Zoom toolbar menu to zoom in or out on a portion of the graph 4 Set the display style for a function 2 ˆ This is optional For multiple equations this helps visually distinguish one from another 5 Define the viewing window 8 Zoom also changes the viewing window 6 Change the graph format if necessary ƒ 9 or 8 Í 7 Graph the selected functions 8 ...

Page 293: ...the Graph mode to FUNCTION Refer to Setting Modes in Operating the Calculator For graphs that do not use complex numbers set Complex Format REAL Otherwise it may affect graphs that use powers such as x1 3 While this module specifically describes y x function graphs the calculator lets you select from six Graph mode settings 1 Press 3 to display the MODE dialog box which shows the current mode sett...

Page 294: ...nd Angle mode check the status line at the bottom of the screen Defining Functions for Graphing In FUNCTION graphing mode you can graph functions named y1 x through y99 x To define and edit these functions use the Y Editor The Y Editor lists function names for POLAR r q polar equations SEQUENCE u n sequences 3D z x y 3D equations DIFFERENTIAL EQUATION y t differential equations Graph Mode Setting ...

Page 295: ...ursor to the entry line 4 Type the expression to define the function The independent variable in function graphing is x The expression can refer to other variables including matrices lists and other functions Only floats and lists of floats will produce a plot Note For an undefined function you do not need to press or When you begin typing the cursor moves to the entry line 5 When you complete the...

Page 296: ... to highlight the function 2 Press or to move the cursor to the entry line 3 Do any of the following Use B and A to move the cursor within the expression and edit it Refer to Editing an Expression in the Entry Line in Operating the Calculator or Press M once or twice to clear the old expression and then type the new one 4 Press The function list now shows the edited function which is automatically...

Page 297: ...e Y Editor To erase Do this A function from the function list Highlight the function and press 0 or M A function from the entry line Press M once or twice depending on the cursor s location and then press All functions Press ƒ and then select 8 Clear Functions When prompted for confirmation press Press To 8 C or 8 D Go to function 1 or to the last defined function respectively If the cursor is on ...

Page 298: ...ction variable Refer to Storing and Recalling Variable Values in Operating the Calculator Creating and Evaluating User Defined Functions in Calculator Home Screen Note User defined functions can have almost any name However if you want them to appear in the Y Editor use function names y1 x y2 x etc Selecting Functions to Graph Regardless of how many functions are defined in the Y Editor you can se...

Page 299: ...ctions from the Home screen or a program To select or deselect Do this A specified function Move the cursor to highlight the function Press This procedure selects a deselected function or deselects a selected function All functions Press to display the All toolbar menu Select the applicable item Selected Deselected If PLOT numbers are displayed those stat plots are selected In this example Plots 1...

Page 300: ...ach defined function you can set a style that specifies how that function will be graphed This is useful when graphing multiple functions For example set one as a solid line another as a dotted line etc Displaying or Changing a Function s Style From the Y Editor 1 Move the cursor to highlight the applicable function 2 Select the Style menu and press 2 ˆ Although the Line item is initially highligh...

Page 301: ...he fifth shaded function reuses the first pattern Style Description Line Connects plotted points with a line This is the default Dot Displays a dot at each plotted point Square Displays a solid box at each plotted point Thick Connects plotted points with a thick line Animate A round cursor moves along the leading edge of the graph but does not leave a path Path A round cursor moves along the leadi...

Page 302: ...played on the Graph screen By setting Window variables you can define the viewing window s boundaries and other attributes Function graphs parametric graphs etc have their own independent set of Window variables Displaying Window Variables in the Window Editor Press 8 to display the Window Editor Window Variables shown in Window Editor Corresponding Viewing Window shown on Graph screen Variable De...

Page 303: ... new one or Press A or B to remove the highlighting then edit the value Values are stored as you type them you do not need to press simply moves the cursor to the next Window variable If you type an expression it is evaluated when you move the cursor to a different Window variable or leave the Window Editor xscl yscl Distance between tick marks on the x and y axes xres Sets pixel resolution 1 thro...

Page 304: ... the cursor s coordinates Function graphs parametric graphs etc have their own independent set of graph formats Displaying Graph Format Settings From the Y Editor Window Editor or Graph screen press ƒ and select 9 Format You also can display the GRAPH FORMATS dialog box from the Y Editor Window Editor or Graph screen Press 8 Í The GRAPH FORMATS dialog box shows the current settings To exit without...

Page 305: ...ng Either Move the cursor to highlight the setting and then press or Press the number for that setting Graph Order Graphs functions one at a time SEQ or all at the same time SIMUL Grid Shows ON or hides OFF grid points that correspond to the tick marks on the axes Axes Shows ON or hides OFF the x and y axes Leading Cursor Shows ON or hides OFF a reference cursor that tracks the functions as they a...

Page 306: ...re ready to graph the selected functions display the Graph screen This screen uses the display style and viewing window that you previously defined Displaying the Graph Screen Press 8 The TI 89 Titanium automatically graphs the selected functions If you select an Zoom operation from the Y Editor or Window Editor the TI 89 Titanium automatically displays the Graph screen Interrupting Graphing While...

Page 307: ...rent boundaries Use a Zoom operation Smart Graph When you display the Graph screen the Smart Graph feature displays the previous window contents immediately provided nothing has changed that requires regraphing Smart Graph updates the window and regraphs only if you have Changed a mode setting that affects graphing a function s graphing attribute a Window variable or a graph format Selected or des...

Page 308: ...he Graph screen no cursor is visible To display the cursor press a cursor pad arrow The cursor moves from the center of the screen and its coordinates are displayed If your screen does not show coordinates set the graph format so that Coordinates RECT or POLAR Press 8 Í To move the free moving cursor Press To an adjoining pixel A cursor pad arrow for any direction y1 x x2 The c indicates these are...

Page 309: ...pears to be on the function it may be near the function but not on it To increase the accuracy Use the Trace tool described on the next page to display coordinates that are on the function Use a Zoom operation to zoom in on a portion of the graph In increments of 10 pixels 2 and then a cursor pad arrow To move the free moving cursor Press Cursor coordinates are for the center of the pixel not the ...

Page 310: ...he cursor s coordinates are displayed at the bottom of the screen If multiple functions are graphed the trace cursor appears on the lowest numbered function selected in the Y Editor The function number is shown in the upper right part of the screen If any stat plots are graphed the trace cursor appears on the lowest numbered stat plot Moving along a Function To move the trace cursor Do this To the...

Page 311: ...s y yn x If the function is undefined at an x value the y value is blank You can continue to trace a function that goes above or below the viewing window You cannot see the cursor as it moves in that off the screen area but the displayed coordinate values show its correct coordinates Note Use QuickCenter to trace a function that goes above or below the window To a specified x value on the function...

Page 312: ...Editor not the appearance of the functions as graphed on the screen Automatic Panning If you trace a function off the left or right edge of the screen the viewing window automatically pans to the left or right There is a slight pause while the new portion of the graph is drawn After an automatic pan the cursor continues tracing Note Automatic panning does not work if stat plots are displayed or if...

Page 313: ...ace even when the cursor is still on the screen Canceling Trace To cancel a trace at any time press N A trace is also canceled when you display another application screen such as the Y Editor When you return to the Graph screen and press to begin tracing If Smart Graph regraphed the screen the cursor appears at the middle x value If Smart Graph does not regraph the screen the cursor appears at its...

Page 314: ...cally displays the Graph screen Procedures for using ZoomBox ZoomIn ZoomOut ZoomStd Memory and SetFactors are given later in this section For more information about the other items refer to the Technical Reference module Zoom Tool Description ZoomBox Lets you draw a box and zoom in on that box ZoomIn ZoomOut Lets you select a point and zoom in or out by an amount defined by SetFactors ZoomDec Sets...

Page 315: ... p 2 1 570796 radians yscl 0 5 or 90 degrees ZoomInt Lets you select a new center point and then sets x and y to 1 and sets xscl and yscl to 10 ZoomData Adjusts Window variables so that all selected stat plots are in view ZoomFit Adjusts the viewing window to display the full range of dependent variable values for the selected functions In function graphing this maintains the current xmin and xmax...

Page 316: ...s The cursor changes to a small square and the screen prompts for 2nd Corner Note To move the cursor in larger increments use 2 B 2 D etc 3 Move the cursor to the opposite corner of the zoom box As you move the cursor the box stretches 4 When you have outlined the area you want to zoom in on press The Graph screen shows the zoomed area You can cancel ZoomBox by pressing N before you press y1 x 2øs...

Page 317: ...variables are multiplied by yFact new xmin xmin ù xFact etc Changing Zoom Factors The Zoom factors define the magnification and reduction used by ZoomIn and ZoomOut 1 From the Zoom menu select 2 ZoomIn or 3 ZoomOut A cursor appears and the screen prompts for New Center 2 Move the cursor to the point where you want to zoom in or out and then press The TI 89 Titanium adjusts the Window variables by ...

Page 318: ...ping or Press A or B to remove the highlighting and then edit the old value 3 Press after typing in an input box you must press twice to save any changes and exit the dialog box Saving or Recalling a Viewing Window After using various Zoom tools you may want to return to a previous viewing window or save the current one Zoom factors must be 1 but they do not have to be integers The default setting...

Page 319: ... From the Zoom menu select 6 ZoomStd Using Math Tools to Analyze Functions On the Graph screen the Math toolbar menu has several tools that help you analyze graphed functions Select To 1 ZoomPrev Return to the viewing window displayed before the previous zoom 2 ZoomSto Save the current viewing window The current Window variable values are stored to the system variables zxmin zxmax etc 3 ZoomRcl Re...

Page 320: ...pt minimum or maximum point within an interval Intersection Finds the intersection of two functions Derivatives Finds the derivative slope at a point f x dx Finds the approximate numerical integral over an interval Inflection Finds the inflection point of a curve where its second derivative changes sign where the curve changes concavity Distance Draws and measures a line between two points on the ...

Page 321: ... or C to move the cursor between functions at the entered x value The corresponding y value is displayed If you press A or B the free moving cursor appears You may not be able to move it back to the entered x value Shade Depends on the number of functions graphed If only one function is graphed this shades the function s area above or below the x axis If two or more functions are graphed this shad...

Page 322: ...se A and B to move the cursor to the lower bound or type its x value 4 Press A 4 at the top of the screen marks the lower bound Finding the Intersection of Two Functions within an Interval 1 From the Graph screen press and select 5 Intersection 2 Select the first function using D or C as necessary and press The cursor moves to the next graphed function 3 Select the second function and press 4 Set ...

Page 323: ...le function Finding the Numerical Integral over an Interval 1 From the Graph screen press and select 7 f x dx 2 As necessary use D and C to select the applicable function Note Typing x values is a quick way to set the limits 6 Set the upper bound and press The cursor moves to the intersection and its coordinates are displayed 3 Set the derivative point Either move the cursor to the point or type i...

Page 324: ...ssary use D and C to select the applicable function 3 Set the lower bound for x Either use A and B to move the cursor to the lower bound or type its x value 4 Press A 4 at the top of the screen marks the lower bound Finding the Distance between Two Points 1 From the Graph screen press and select 9 Distance 5 Set the upper limit and press The interval is shaded and its approximate numerical integra...

Page 325: ...he second point If you use the cursor to set the point a line is drawn as you move the cursor Drawing a Tangent Line 1 From the Graph screen press and select A Tangent 2 As necessary use D and C to select the applicable function Note To erase a drawn tangent line press ReGraph 7 Press The distance between the two points is displayed along with the connecting line 3 Set the tangent point Either mov...

Page 326: ...rst point Shading the Area between a Function and the x Axis You must have only one function graphed If you graph two or more functions the Shade tool shades the area between two functions 1 From the Graph screen press and select C Shade The screen prompts for Above X axis 2 Select one of the following To shade the function s area Above the x axis press Below the x axis press j N 5 Set the second ...

Page 327: ... an Interval You must have at least two functions graphed If you graph only one function the Shade tool shades the area between the function and the x axis 1 From the Graph screen press and select C Shade The screen prompts for Above 2 As necessary use D or C to select a function Shading will be above this function 3 Press The cursor moves to the next graphed function and the screen prompts for Be...

Page 328: ...If you do not press A or B or type an x value when setting the lower and upper bound xmin and xmax will be used as the lower and upper bound respectively 7 Press A 4 at the top of the screen marks the lower bound 8 Set the upper bound and press The bounded area is shaded To erase the shaded area press ReGraph Below function Above function ...

Page 329: ...c Function Graphing Any differences that apply to polar equations are described on the following pages Graphing Polar Equations 1 Set Graph mode 3 to POLAR Also set Angle mode if necessary 2 Define x and y components on Y Editor 8 3 Select which defined equations to graph Select the x or y component or both Note To turn off any stat data plots press 5 or use to deselect them ...

Page 330: ...point by tracing a polar equation 4 Set the display style for an equation You can set either the x or y component 2 ˆ This is optional For multiple equations this helps visually distinguish one from another 5 Define the viewing window 8 Zoom also changes the viewing window 6 Change the graph format if necessary ƒ 9 or 8 Í 7 Graph the selected equations 8 ...

Page 331: ... functions as described in Basic Function Graphing This section describes the differences that apply to polar equations Setting the Graph Mode Use 3 to set Graph POLAR before you define equations or set Window variables The Y Editor and the Window Editor let you enter information for the current Graph mode setting only You should also set the Angle mode to the units RADIAN or DEGREE you want to us...

Page 332: ...uations When you return to FUNCTION graphing mode your y x functions are still defined in the Y Editor When you return to POLAR graphing mode your r q equations are still defined Selecting the Display Style The Above and Below styles are not available for polar equations and are dimmed on the Y Editor s Style toolbar menu Window Variables The Window Editor maintains an independent set of Window va...

Page 333: ...s are plotted Setting the Graph Format To display coordinates as r and q values use qstep Increment for the q value Polar equations are evaluated at r qmin r qmin qstep r qmin 2 qstep not to exceed r qmax xmin xmax ymin ymax Boundaries of the viewing window xscl yscl Distance between tick marks on the x and y axes qmin 0 xmin L10 ymin L10 qmax 2p 6 2831853 radians or 360 degrees xmax 10 ymax 10 qs...

Page 334: ... graphing you can explore a graph by using the following tools Any displayed coordinates are shown in polar or rectangular form as set in the graph format Tool For Polar Graphs Free Moving Cursor Works just as it does for function graphs Zoom Works just as it does for function graphs Only x xmin xmax xscl and y ymin ymax yscl Window variables are affected The q Window variables qmin qmax qstep are...

Page 335: ...t or right press to center the viewing window on the cursor location Automatic panning is not available If you move the cursor off the left or right side of the screen the TI 89 Titanium Voyage 200 graphing calculator will not automatically pan the viewing window However you can use QuickCenter Math Only 1 Value 6 Derivatives 9 Distance A Tangent and B Arc are available for polar graphs These tool...

Page 336: ...asic Function Graphing Any differences that apply to parametric equations are described on the following pages Graping Parametic Equations 1 Set Graph mode 3 to PARAMETRIC Also set Angle mode if necessary 2 Define x and y components on Y Editor 8 3 Select which defined equations to graph Select the x or y component or both Note To turn off any stat data plots press 5 or use to deselect them ...

Page 337: ...point by tracing a parametric equation 4 Set the display style for an equation You can set either the x or y component 2 ˆ This is optional For multiple equations this helps visually distinguish one from another 5 Define the viewing window 8 Zoom also changes the viewing window 6 Change the graph format if necessary ƒ 9 or 8 Í 7 Graph the selected equations 8 ...

Page 338: ...ply to parametric equations Setting the Graph Mode Use 3 to set Graph PARAMETRIC before you define equations or set Window variables The Y Editor and the Window Editor let you enter information for the current Graph mode setting only Defining Parametric Equations on the Y Editor To graph a parametric equation you must define both its x and y components If you define only one component the equation...

Page 339: ... return to FUNCTION graphing mode your y x functions are still defined in the Y Editor When you return to PARAMETRIC graphing mode your x and y components are still defined Selecting Parametric Equations To graph a parametric equation select either its x or y component or both When you enter or edit a component it is selected automatically Selecting x and y components separately can be useful for ...

Page 340: ...r menu Window Variables The Window Editor maintains an independent set of Window variables for each Graph mode setting just as the Y Editor maintains independent function lists Parametric graphs use the following Window variables Note You can use a negative tstep If so tmin must be greater than tmax Variable Description tmin tmax Smallest and largest t values to evaluate tstep Increment for the t ...

Page 341: ...following tools Note During a trace you can also evaluate x t and y t by typing the t value and pressing You can use QuickCenter at any time during a trace even if the cursor is still on the screen xscl yscl Distance between tick marks on the x and y axes tmin 0 xmin L10 ymin L10 tmax 2p 6 2831853 radians or 360 degrees xmax 10 ymax 10 tstep p 24 1308996 radians or 7 5 degrees xscl 1 yscl 1 Tool F...

Page 342: ...ter applies to all directions If you move the cursor off the screen top or bottom left or right press to center the viewing window on the cursor location Automatic panning is not available If you move the cursor off the left or right side of the screen the TI 89 Titanium will not automatically pan the viewing window However you can use QuickCenter Math Only 1 Value 6 Derivatives 9 Distance A Tange...

Page 343: ...are described on the following pages Graphing Sequences 1 Set Graph mode 3 to SEQUENCE Also set Angle mode if necessary 2 Define sequences and if needed initial values on Y Editor 8 3 Select which defined sequences to graph Do not select initial values Note To turn off any stat data plots press 5 or use to deselect them 4 Set the display style for a sequence 2 ˆ For sequences the default style is ...

Page 344: ... out on a portion of the graph Use the Math toolbar menu to evaluate a sequence Only 1 Value is available for sequences Plot sequences on Time the default Web or Custom axes Note You can also evaluate a sequence while tracing Simply enter the n value directly from the keyboard 5 Define the viewing window 8 Zoom also changes the viewing window 6 Change the graph format if necessary 9 or 8 Í 7 Graph...

Page 345: ...uences or set Window variables The Y Editor and the Window Editor let you enter information for the current Graph mode setting only Defining Sequences on the Y Editor If a sequence requires more than one initial value enter them as a list enclosed in braces and separated by commas You must use a list to enter two or more initial values You can define sequences u1 n through u99 n Use ui only for re...

Page 346: ...aphing mode you define a set of y x functions You change to SEQUENCE graphing mode and define a set of u n sequences When you return to FUNCTION graphing mode your y x functions are still defined in the Y Editor When you return to SEQUENCE graphing mode your u n sequences are still defined Note You can use the Define command from the Home screen see Technical Reference to define functions and equa...

Page 347: ... defined sequences are evaluated even if they are not plotted With CUSTOM axes when you specify a sequence in the custom settings it is graphed regardless of whether it is selected Selecting the Display Style Only the Line Dot Square and Thick styles are available for sequence graphs Dot and Square mark only those discrete integer values in plotstep increments at which a sequence is plotted You ca...

Page 348: ...est n values to evaluate Sequences are evaluated at u nmin u nmin 1 u nmin 2 not to exceed u nmax plotStrt The term number that will be the first one plotted depending on plotstep For example to begin plotting with the 2nd term in the sequence set plotstrt 2 The first term will be evaluated at nmin but not plotted plotStep Incremental n value for graphing only This does not affect how the sequence...

Page 349: ...ent points are plotted To see how plotstrt affects graph look at the following examples of a recursive sequence Note Both of these graphs use the same Window variables except for plotstrt nmin 1 nmax 10 plotstrt 1 plotstep 1 xmin L10 xmax 10 xscl 1 ymin L10 ymax 10 yscl 1 This graph is plotted beginning with the 1st term This graph is plotted beginning with the 9th term plotStrt 1 plotStrt 9 ...

Page 350: ...iple sequences are always plotted simultaneously With WEB axes multiple sequences are always plotted sequentially Exploring a Graph As in function graphing you can explore a graph by using the following tools Any displayed coordinates are shown in rectangular or polar form as set in the graph format You could set xmin first n value to graph xmax nmax although you can use other values ymin and ymax...

Page 351: ...e approximately ten plotted points at a time press 2 B or 2 A When you begin a trace the cursor is on the first selected sequence at the term number specified by plotstrt even if it is outside the viewing window QuickCenter applies to all directions If you move the cursor off the screen top or bottom left or right press to center the viewing window on the cursor location With WEB axes the trace cu...

Page 352: ... graph Examples of the different types are given later in this module Displaying the AXES Dialog Box From the Y Editor Axes Depending on the current Axes setting some items may be dimmed To exit without making any changes press N Item Description Axes TIME Plots u n on the y axis and n on the x axis WEB Plots u n on the y axis and u nN1 on the x axis CUSTOM Lets you select the x and y axes Build W...

Page 353: ...nce s behavior Valid Functions for Web Plots A sequence must meet the following criteria otherwise it will not be graphed properly on WEB axes The sequence Must be recursive with only one recursion level u nN1 but not u nN2 Cannot reference n directly Cannot reference any other defined sequence except itself When You Display the Graph Screen After you select WEB axes and display the Graph screen t...

Page 354: ...ed the web may be displayed manually or automatically depending on how you set Build Web on the AXES dialog box The web 1 Starts on the x axis at the initial value ui when plotstrt 1 2 Moves vertically either up or down to the sequence If Build Web The web is TRACE Not drawn until you press The web is then drawn step by step as you move the trace cursor you must have an initial value before using ...

Page 355: ...b moves to the sequence plotStep is ignored Example Convergence 1 On the Y Editor 8 define u1 n L 8u1 nN1 3 6 Set initial value ui1 L4 2 Set Axes TIME 3 On the Window Editor 8 set the Window variables 5 On the Y Editor set Axes WEB and Build Web AUTO nmin 1 nmax 25 plotstrt 1 plotstep 1 xmin 0 xmax 25 xscl 1 ymin L10 ymax 10 yscl 1 4 Graph the sequence 8 By default a sequence uses the Square displ...

Page 356: ...c approach the convergence point Note When the nc value changes the cursor is on the sequence The next time you press B nc stays the same but the cursor is now on the y x reference line nmin 1 nmax 25 plotstrt 1 plotstep 1 xmin L10 xmax 10 xscl 1 ymin L10 ymax 10 yscl 1 7 Regraph the sequence Web plots are always shown as lines regardless of the selected display style Note During a trace you can m...

Page 357: ... 5 On the Y Editor set Axes WEB and Build Web AUTO 6 On the Window Editor 8 set the Window variables nmin 0 nmax 10 plotstrt 1 plotstep 1 xmin 0 xmax 10 xscl 1 ymin L75 ymax 10 yscl 1 4 Graph the sequence 8 Because the sequence quickly diverges to large negative values only a few points are plotted nmin 0 nmax 10 plotstrt 1 plotstep 1 xmin L10 xmax 10 xscl 1 ymin L10 ymax 10 yscl 1 u n n ...

Page 358: ...ME 3 On the Window Editor 8 set the Window variables 5 On the Y Editor set Axes WEB and Build Web AUTO 7 Regraph the sequence The web plot shows how quickly the sequence diverges to large negative values nmin 1 nmax 100 plotstrt 1 plotstep 1 xmin 0 xmax 100 xscl 10 ymin 0 ymax 5 yscl 1 4 Graph the sequence 8 Note Compare this graph with the divergence example This is the same sequence with a diffe...

Page 359: ...n in the following example CUSTOM axes are particularly effective for showing relationships between one sequence and another nmin 1 nmax 100 plotstrt 1 plotstep 1 xmin 2 68 xmax 6 47 xscl 1 ymin 4 7 ymax 47 yscl 1 7 Regraph the sequence Note The web moves to an orbit oscillating between two stable points 9 On the Window Editor set plotstrt 50 Then regraph the sequence Note By starting the web plot...

Page 360: ...s for Rn and Wn u1 n u1 nN1 1 05 N 001 u2 nN1 ui1 200 u2 n u2 nN1 1 0002 u1 nN1 N 03 ui2 50 Note Assume there are initially 200 rabbits and 50 foxes 2 Set Axes TIME R Number of rabbits M Growth rate of rabbits if there are no foxes use 05 K Rate at which foxes can kill rabbits use 001 W Number of foxes G Growth rate of foxes if there are rabbits use 0002 D Death rate of foxes if there are no rabbi...

Page 361: ...trt 1 plotstep 1 xmin 0 xmax 400 xscl 100 ymin 0 ymax 300 yscl 100 4 Graph the sequence 8 Note Use to individually trace the number of rabbits u1 n and foxes u2 n over time n nmin 0 nmax 400 plotstrt 1 plotstep 1 xmin 84 xmax 237 xscl 50 ymin 25 ymax 75 yscl 10 7 Regraph the sequence Note Use to trace both the number of rabbits xc and foxes yc over the cycle of 400 generations u n u1 n u2 n u2 n u...

Page 362: ...xample Fibonacci Sequence In a Fibonacci sequence the first two terms are 1 and 1 Each succeeding term is the sum of the two immediately preceding terms 1 On the Y Editor 8 define the sequence and set the initial values as shown 2 Set table parameters 8 to tblStart 1 tbl 1 Independent AUTO You must enter 1 1 although 1 1 is shown in the sequence list This item is dimmed if you are not using TIME a...

Page 363: ...uence Graphing 360 3 Set Window variables 8 so that nmin has the same value as tblStart 4 Display the table 8 5 Scroll down the table D or 2 D to see more of the sequence Fibonacci sequence is in column 2 ...

Page 364: ...equations are described on the following pages Graphing 3D Equations 1 Set Graph mode 3 to 3D Also set Angle mode if necessary 2 Define 3D equations on Y Editor 8 3 Select which equation to graph You can select only one 3D equation To turn off any stat data plots press 5 or use to deselect them 4 Define the viewing cube 8 For 3D graphs the viewing window is called the viewing cube Zoom also change...

Page 365: ... the Math toolbar menu to evaluate the equation at a specified point Only 1 Value is available for 3D graphs You can also evaluate z x y while tracing Type the x value and press then type the y value and press 5 Change the graph format if necessary ƒ 9 or 8 Í Note To help you see the orientation of 3D graphs turn on Axes and Labels 6 Graph the selected equations 8 Note Before displaying the graph ...

Page 366: ...3D before you define equations or set Window variables The Y Editor and the Window Editor let you enter information for the current Graph mode setting only Defining 3D Equations on the Y Editor The Y Editor maintains an independent function list for each Graph mode setting For example suppose In FUNCTION graphing mode you define a set of y x functions You change to 3D graphing mode and define a se...

Page 367: ... Selecting the Display Style Because you can graph only one 3D equation at a time display styles are not available On the Y Editor the Style toolbar menu is dimmed For 3D equations however you can use ƒ 9 or 8 Í to set the Style format to WIRE FRAME or HIDDEN SURFACE Window Variables The Window Editor maintains an independent set of Window variables for each Graph mode setting just as the Y Editor...

Page 368: ...t where the grid lines or grid wires intersect The incremental value along x and y is calculated as x increment y increment The number of grid wires is xgrid 1 and ygrid 1 For example when xgrid 14 and ygrid 14 the xy grid consists of 225 15 15 grid points ncontour The number of contours evenly distributed along the displayed range of z values Variable Description xmax xmin xgrid ymax ymin ygrid z...

Page 369: ... to ensure that enough points are plotted Note Increasing the grid variables decreases the graphing speed Setting the Graph Format The Axes and Style formats are specific to the 3D graphing mode Exploring a Graph As in function graphing you can explore a graph by using the following tools Any displayed coordinates are shown in rectangular or cylindrical form as set in the graph format In 3D graphi...

Page 370: ...affected The grid xgrid ygrid and eye eyeq eyef eyeψ Window variables are not affected unless you select 6 ZoomStd which resets these variables to their standard values Trace Lets you move the cursor along a grid wire from one grid point to the next on the 3D surface When you begin a trace the cursor appears at the midpoint of the xy grid QuickCenter is available At any time during a trace regardl...

Page 371: ...he x and y axes have a different orientation than other graphing modes How to Move the Cursor On a 3D surface the cursor always follows along a grid wire Math Only 1 Value is available for 3D graphs This tool displays the z value for a specified x and y value After selecting 1 Value type the x value and press Then type the y value and press Cursor Key Moves the cursor to the next grid point in the...

Page 372: ...ir labels from the Y Editor Window Editor or Graph screen use 8 Í Simple Example of Moving the Cursor The following graph shows a sloped plane that has the equation z1 x y M x y 2 Suppose you want to trace around the displayed boundary In 2D graphing the x and y axes always have the same orientation relative to the Graph screen In 3D graphing x and y have a different orientation relative to the Gr...

Page 373: ...ross the grid Notice that the grid wires may not appear parallel to the axes Example of the Cursor on a Hidden Surface On more complex shapes the cursor may appear as if it is not on a grid point This is an optical illusion caused when the cursor is on a hidden surface D moves in a negative y direction back to ymin B moves in a positive x direction up to xmax A moves in a negative x direction back...

Page 374: ... negative x values Example of an Off the Curve Cursor Although the cursor can move only along a grid wire you will see many cases where the cursor does not appear to be on the 3D surface at all This occurs when the z axis is too short to show z x y for the corresponding x and y values You can move the cursor so that it does not appear to be on a grid point If you cut away the front side you can se...

Page 375: ...the viewing cube Note QuickCenter lets you center the viewing cube on the cursor s location Simply press When zc is outside the z boundary of the viewing cube the cursor is physically displayed at zmin or zmax although the screen shows the correct trace coordinates Rotating and or Elevating the Viewing Angle In 3D graphing mode the eyeq and eyef Window variables let you set viewing angles that det...

Page 376: ...enter eyeq eyef and eyeψ in degrees regardless of the current angle mode The viewing angle has three components eyeq angle in degrees from the positive x axis eyef angle in degrees from the positive z axis eyeψ angle in degrees by which the graph is rotated counter clockwise around the line of sight set by eyeq and eyef Y Z X eyeq eyef eye Do not enter a symbol For example type 20 70 and 0 not 20 ...

Page 377: ... the Graph screen is always oriented along the viewing angle From this point of view you can change eyeq to rotate the viewing angle around the z axis Note This example increments eyeq by 30 z1 x y x3 y y3 x 390 In this example eyef 70 eyeq 20 eyeq 50 eyeq 80 ...

Page 378: ...plane Note This example starts on the xy plane eyef 90 and decrements eyef by 20 to elevate the viewing angle Effect of Changing eyeψ psi The view on the Graph screen is always oriented along the viewing angles set by eyeq and eyef You can change eyeψ to rotate the graph around that line of sight z1 x y x3 y y3 x 390 In this example eyeq 20 eyef 90 eyef 70 eyef 50 ...

Page 379: ...en s width and height This causes some distortion as shown in the example z1 x y x3 y y3 x 390 In this example eyeq 20 and eyef 70 eyeψ 0 eyeψ 45 eyeψ 90 When eyeψ 0 the z axis runs the height of the screen When eyeψ 90 the z axis runs the width of the screen z 10 z ë10 z 10 z ë10 ...

Page 380: ... store to these variables as necessary Animating a 3D Graph Interactively After plotting any 3D graph you can change the viewing angle interactively by using the cursor The Viewing Orbit When using A and B to animate a graph think of it as moving the viewing angle along its viewing orbit around the graph To type f or ψ press 8 c j F or 8 c Ú respectively You can also press 2 G and use the Greek me...

Page 381: ...along the viewing orbit A or B Change the viewing orbit s elevation primarily increases or decreases eyef C or D Animate the graph continuously Press and hold the cursor for about 1 second and then release it To stop press N or 8 space Change between 4 animation speeds increase or decrease the incremental changes in the eye Window variables Press or Change the viewing angle of a non animated graph...

Page 382: ...raph pictures and then flipping or cycling through those pictures Refer to Animating a Series of Graph Pictures Additonal Graphing Topics This method gives you more control over the Window variable values particularly eyeψ which rotates the graph Changing the Axes and Style Formats With its default settings the TI 89 Titanium displays hidden surfaces on a 3D graph but does not display the axes How...

Page 383: ... not at a corner For example if xmin ymin zmin L10 and xmax ymax zmax 10 the origin is at the center of the box The dialog box shows the current graph format settings To exit without making a change press N To display the valid Axes settings highlight the current setting and press B AXES Shows standard xyz axes BOX Shows 3 dimensional box axes The edges of the box are determined by the Window vari...

Page 384: ...ots Be Aware of Possible Optical Illusions The eye angles used to view a graph eyeq eyef and eyeψ Window variables can result in optical illusions that cause you to lose perspective on a graph Typically most optical illusions occur when the eye angles are in a negative quadrant of the coordinate system To display the valid Style settings highlight the current setting and press B WIRE FRAME Shows t...

Page 385: ...t displayed on the screen to show the front of the box To minimize the effect of optical illusions use the GRAPH FORMATS dialog box to set Style HIDDEN SURFACE Contour Plots In a contour plot a line is drawn to connect adjacent points on the 3D graph that have the same z value This module discusses the CONTOUR LEVELS and WIRE AND CONTOUR graph format styles Looking down from above the xy plane Loo...

Page 386: ...own the z axis You can change the viewing angle as necessary The graph is shown in expanded view To switch between expanded and normal view press p The Labels format is set to OFF automatically For WIRE AND CONTOUR the contours are drawn on a wire frame view The viewing angle view expanded or normal and Labels format retain their previous settings Notes From the Graph screen you can switch from on...

Page 387: ...ariable values as a ZoomStd viewing cube If you use ZoomStd press Z to look down the z axis Do not confuse the contours with the grid lines The contours are darker Style z1 x y x3 y y3 x 390 z1 x y x2 5y2 5 Looking down z axis CONTOUR LEVELS Using eyeq 20 eyef 70 eyeψ 0 CONTOUR LEVELS WIRE AND CONTOUR ...

Page 388: ... the standard viewing window zmin L10 and zmax 10 the increment is 3 333 Five contours are drawn for z L6 666 L3 333 0 3 333 and 6 666 Note however that a contour is not drawn for a z value if the 3D graph is not defined at that z value increment The z values for the contours are zmin increment zmin 2 increment zmin 3 increment zmin ncontour increment zmax zmin ncontour 1 The default is 5 You can ...

Page 389: ...ther Type the point s x value and press and then type the y value and press or Move the cursor to the applicable point The cursor moves along the grid lines Then press For example suppose the current graph is z1 x y x2 5y2 5 If you specify x 2 and y 3 a contour is drawn for z 3 5 Note Any existing contours remain on the graph To remove the default contours display the Window editor 8 and set ncont...

Page 390: ...e current 3D graph A contour is not drawn if the specified z value is outside the viewing cube or if the 3D graph is not defined at that z value Notes about Contour Plots For a contour plot You can use the cursor keys to animate the contour plot You cannot trace the contours themselves However you can trace the wire frame as seen when Style WIRE AND CONTOUR It may take awhile to evaluate the equat...

Page 391: ...set Style CONTOUR LEVELS or WIRE AND CONTOUR 8 Í Example Contours of a Complex Modulus Surface The complex modulus surface given by z a b abs f a bi shows all the complex zeros of any polynomial y f x Example In this example let f x x3 1 By substituting the general complex form x yi for x you can express the complex surface equation as z x y abs x y i 3 1 1 Use 3 to set Graph 3D 2 Press 8 and defi...

Page 392: ... and i 4 Display the Graph Formats dialog box 8 Í Turn on the axes set Style CONTOUR LEVELS and return to the Window editor 6 Press and move the trace cursor to the zero in the fourth quadrant The coordinates let you estimate 428 857i as the zero 7 Press N Then use the cursor keys to animate the graph and view it from different eye angles This example shows eyeq 70 eyef 70 and eyeψ 0 1 1 2 3 2 1 2...

Page 393: ...ay to graph 2D implicit forms that cannot be graphed in function graphing mode Technically an implicit plot is a 3D contour plot with a single contour drawn for z 0 only Explicit and Implicit Forms In 2D function graphing mode equations have an explicit form y f x where y is unique for each value of x Many equations however have an implicit form f x y g x y where you cannot explicitly solve for y ...

Page 394: ...ate equation and graph it as you would any 3D equation with the following exception Display the GRAPH FORMATS dialog box from the Y Editor Window editor or Graph screen 8 Í Rearrange the implicit form as an equation set to zero f x y g x y 0 In the Y Editor enter the non zero side of the equation This is valid because an implicit plot automatically sets the equation equal to zero z1 x y f x y g x ...

Page 395: ... set initially so that you are viewing the plot by looking down the z axis You can change the viewing angle as necessary The plot is shown in expanded view To switch between expanded and normal view press p The Labels format is set to OFF automatically and then set Style IMPLICIT PLOT Style x2 y2 4 z1 x y x2 y2 4 sin x cos y e xùy z1 x y sin x cos y e xùy IMPLICIT PLOT ...

Page 396: ...ot itself However you can trace the unseen wire frame graph of the 3D equation It may take awhile to evaluate the equation initially Because of possible long evaluation times you first may want to experiment with your 3D equation by using Style WIRE FRAME The evaluation time is much shorter Then after you re sure you have the correct Window variable values set Style IMPLICIT PLOT 8 Í Example Impli...

Page 397: ...efine the equation z1 x y sin x 4 y x 3y 1 3 Press 8 and set the Window variables as shown 4 Press 8 ÍTurn on the axes set Style IMPLICIT PLOT and return to the Window editor 5 Press 8 to graph the equation It will take awhile to evaluate the graph so be patient The graph shows where sin x4 y x3y 1 ...

Page 398: ...tween normal and expanded views 6 Use the cursor keys to animate the graph and view it from different eye angles Note For more detail increase the xgrid and ygrid Window variables However this increases the graph evaluation time In expanded view this example shows eyeq L127 85 eyef 52 86 and eyeψ L18 26 ...

Page 399: ... y x functions as described in Basic Function Graphing Any differences are described on the following pages Graphing Differential Equations 1 Set Graph mode 3 to DIFF EQUATIONS Also set Angle mode if necessary 2 Define equations and optionally initial conditions on Y Editor 8 3 Select which defined functions to graph Note To turn off any stat data plots press 5 or use to deselect them ...

Page 400: ...s 9 or 8 Í Note The Fields format is critical depending on the order of the equation 6 Set the axes as applicable depending on the Fields format 2 Note Valid Axes settings depend on the Fields format 7 Define the viewing window 8 Note Depending on the Solution Method and Fields formats different Window variables are displayed Zoom also changes the viewing window ...

Page 401: ...ONS before you define differential equations or set Window variables The Y Editor and the Window Editor let you enter information for the current Graph mode setting only Defining Differential Equations on the Y Editor 8 Graph the selected functions 8 Use t0 to specify when initial conditions occur You can also set t0 in the Window Editor Use yi to specify one or more initial conditions for the cor...

Page 402: ...ons you must enter them as a system of 1st order equations Detailed information is available on setting initial conditions Selecting Differential Equations Important Selecting y1 will graph the y1 solution curve not the derivative y1 depending on the axis setting Enter y1 001y1ù 100Ny1 Not y1 001y1 t ù 100Ny1 t Do not use implied multiplication between a variable and parenthetical expression If yo...

Page 403: ...fected by differential equations are From the Y Editor Window Editor or Graph screen press 9 or 8 Í Graph format Description Graph Order Not available Solution Method Specifies the method used to solve the differential equations RK Runge Kutta method For information about the algorithm used for this method refer to the Technical Reference module EULER Euler method The method lets you choose either...

Page 404: ...s whether to draw a field for the differential equation SLPFLD Draws a slope field for only one 1st order equation with t on the x axis and the solution on the y axis DIRFLD Draws a direction field for only one 2nd order equation or system of two 1st order equations with axes determined by the custom axes settings FLDOFF Does not display a field This is valid for equations of any order but you mus...

Page 405: ...ted differential equations on the y axis CUSTOM Lets you select the x and y axes Variable Description t0 Time at which the initial conditions entered in the Y Editor occur You can set t0 in the Window Editor and Y Editor If you set t0 in the Y Editor tplot is set to the same value automatically tmax tstep Used to determine the t values where the equations are plotted y t0 y t0 tstep y t0 2ùtstep n...

Page 406: ...starting at t0 may not be interesting visually By setting tplot greater than t0 you can start the plot at the interesting area which speeds up the graphing time and avoids unnecessary clutter on the Graph screen Variable Description xmin xmax ymin ymax Boundaries of the viewing window xscl yscl Distance between tick marks on the x and y axes ncurves Number of solution curves 0 through 10 that will...

Page 407: ...d by the RK method to help select a step size for solving the equation must be 1EL14 fldres Fields SLPFLD or DIRFLD only Number of columns 1 through 80 used to draw a slope or direction field across the full width of the screen Estep Solution Method EULER only Euler iterations between tstep values must be an integer 0 For more accuracy you can increase Estep without plotting additional points dtim...

Page 408: ...89 Titanium reuses the picture in fldpic instead of having to redraw the field This can speed up the regraphing time significantly fldpic is deleted automatically when you exit the differential equation graphing mode or when you display a graph with Fields FLDOFF Exploring a Graph As in function graphing you can explore a graph by using the following tools Any displayed coordinates are shown in re...

Page 409: ...move approximately ten plotted points at a time press 2 B or 2 A If you enter initial conditions in the Y Editor or let the ncurves Window variable plot curves automatically you can trace the curves If you use 2 Š IC from the Graph screen to select initial conditions interactively you cannot trace the curves QuickCenter applies to all directions If you move the cursor off the screen top or bottom ...

Page 410: ... enclosed in braces and separated by commas For a 2nd or higher order differential equation you must define a system of 1st order equations in the Y Editor To enter initial conditions for the y1 equation use the yi1 line etc If you enter initial conditions you must enter the same number of initial conditions for each equation in the system Otherwise a Dimension error occurs To specify when the ini...

Page 411: ...set temporarily at the middle of the Graph screen However the value of t0 as set in the Y Editor or Window Editor is not changed Notes Without entering initial conditions use SLPFLD with ncurves 0 or DIRFLD to display a slope or direction field only SLPFLD is for a single 1st order equation only DIRFLD is for a 2nd order equation or system of two 1st order equations only If Fields Then SLPFLD Uses...

Page 412: ...Fields Do this SLPFLD or DIRFLD Press 2 Š Specify an initial condition Either Move the cursor to the applicable point and press or For each of the two coordinates type a value and press For SLPFLD 1st order only enter values for t0 and y t0 For DIRFLD 2nd order or system of two 1st order equations only enter values for both y t0 initial conditions where t0 is the value set in the Y Editor or Windo...

Page 413: ... about Tracing a Solution Curve When you enter initial conditions in the Y Editor or let ncurves graph solution curves automatically you can use to trace the curves However you cannot trace a curve drawn by selecting an initial condition interactively These curves are drawn not plotted FLDOFF Press 2 Š You are prompted to select the axes for which you want to enter initial conditions Your selectio...

Page 414: ...n into a 1st Order System A system of equations can be defined in various ways but the following is a general method 1 Rewrite the original differential equation as necessary a Solve for the highest ordered derivative b Express it in terms of y and t c On the right side of the equation only substitute to eliminate any references to derivative values Note To produce a 1st order equation the right s...

Page 415: ...ft side of the equation substitute for the derivative value as shown below In place of Substitute y y y y y 4 y1 y2 y3 y4 y5 y et N y2 N y1 Do not substitute on the left side at this time In place of Substitute y y y y 4 y1 y2 y3 y4 y2 et N y2 N y1 ...

Page 416: ...e solution to the nth order equation You may want to deselect any other equations in the system Example of a 2nd Order Equation The 2nd order differential equation y y 0 represents a simple harmonic oscillator Transform this into a system of equations for the Y Editor Then graph the solution for initial conditions y 0 0 and y 0 1 2 On the applicable lines in the Y Editor define the system of equat...

Page 417: ...em of equations 4 Enter the initial conditions yi1 0 and yi2 1 Note t0 is the time at which the initial conditions occur It is also the first t evaluated for the graph By default t0 0 5 Press 9 or 8 Í and set Axes ON Labels OFF Solution Method RK and Fields DIRFLD Important For 2nd order equations you must set Fields DIRFLD or FLDOFF y y 0 y Ly y Ly1 y2 Ly1 yi1 is the initial condition for y 0 yi2...

Page 418: ...s 2 and make sure Axes CUSTOM with y1 and y2 as the axes Important Fields DIRFLD cannot plot a time axis An Invalid Axes error occurs if Axes TIME or if t is set as a CUSTOM axis 7 In the Window Editor 8 set the Window variables t0 0 tmax 10 tstep 1 tplot 0 xmin L2 xmax 2 xscl 1 ymin L2 ymax 2 yscl 1 ncurves 0 diftol 001 fldres 14 dtime 0 8 Display the Graph screen 8 x axis y1 y y axis y2 y ...

Page 419: ...splay different graphs in both parts of a split screen you must use the 2 graph mode 10 Press 2 a to switch to the right side of the split screen 11 Use to select y1 and y2 The right side uses the same equations as the left side However no equations are selected initially in the right side 12 Press 9 or 8 Í Set Fields FLDOFF Important Because Fields DIRFLD cannot plot a time axis you must change t...

Page 420: ...Window Editor change ymin and ymax as shown to the right Note When you enter 2 graph mode Window variables for the right side are set to their defaults ymin L2 ymax 2 15 Press 8 to display the Graph screen for graph 2 The left side shows the phase plane orbit The right side shows the solution curve and its derivative 16 To return to a full screen of the original graph press 2 a to switch to the le...

Page 421: ... x N 2y N 2y N y y sin t N 2y N 2y N y y sin t N 2y3 N 2y2 N y1 y3 sin t N 2y3 N 2y2 N y1 3 In the Y Editor 8 enter the system of equations 4 Enter the initial conditions yi1 0 yi2 1 and yi3 1 Note t0 is the time at which the initial conditions occur By default t0 0 5 Be sure that only y1 is selected Use to deselect any other equations Important The solution to the y1 equation is the solution to t...

Page 422: ... you must set Fields FLDOFF Otherwise an Undefined variable error occurs when graphing 7 In the Y Editor press 2 Set Axes TIME Note With Axes TIME the solution to the selected equation is plotted against time t 8 In the Window Editor 8 set the Window variables t0 0 tmax 10 tstep 1 tplot 0 xmin L1 xmax 10 xscl 1 ymin L3 ymax 3 yscl 1 ncurves 0 diftol 001 ...

Page 423: ...for showing different kinds of relationships Displaying the AXES Dialog Box From the Y Editor press 2 9 Display the Graph screen 8 Note To find the solution at a particular time use to trace the graph If Fields SLPFLD Axes is unavailable 2 Item Description Axes TIME Plots t on the x axis and y solutions to all selected differential equations on the y axis CUSTOM Lets you select the x and y axes ...

Page 424: ...olution using both time and custom axes X Axis Y Axis Active only when Axes CUSTOM these let you select what you want to plot on the x and y axes t time y solutions y1 y2 etc of all selected differential equations y values of all selected differential equations y1 y2 etc y1 y2 etc the solution to the corresponding differential equation regardless of whether that equation is selected y1 y2 etc the ...

Page 425: ... 2 y2 Population of rabbits yi2 Initial population of rabbits 5 1 Use 3 to set Graph DIFF EQUATIONS 2 In the Y Editor 8 define the differential equations and enter the initial conditions Note To speed up graphing times clear any other equations in the Y Editor With FLDOFF all equations are evaluated even if they are not selected 3 Press 9 or 8 Í Set Axes ON Labels ON Solution Method RK and Fields ...

Page 426: ...bles t0 0 tmax 10 tstep p 24 tplot 0 xmin L1 xmax 10 xscl 5 ymin L10 ymax 40 yscl 5 ncurves 0 diftol 001 6 Graph the differential equations 8 7 Press to trace Then press 3 to see the number of foxes yc for y1 and rabbits yc for y2 at t 3 Note Use C and D to move the trace cursor between the curves for y1 and y2 y2 t y1 t ...

Page 427: ... a 2nd order equation 9 Press 2 Confirm that the axes are set as shown 10 In the Y Editor clear the initial conditions for yi1 and yi2 11 Return to the Graph screen which displays only the direction field 12 To graph a family of solutions return to the Y Editor and enter the initial conditions shown below yi1 2 6 7 and yi2 5 12 18 Note Use a list to specify more than one initial condition ...

Page 428: ...tion methods Then plot those points along with a graph of the equation s exact solution Example 13 Return to the Graph screen which displays a curve for each pair of initial conditions 14 Press to trace Then press 3 to see the number of foxes xc and rabbits yc at t 3 Because t0 0 and tmax 10 you can trace in the range 0 t 10 Note Use C and D to move the trace cursor from one initial condition curv...

Page 429: ...tion Method RK and Fields FLDOFF Note To speed up graphing times clear any other equations in the Y Editor With FLDOFF all equations are evaluated even if they are not selected 6 In the Window Editor 8 set the Window variables Do not use implied multiplication between the variable and parentheses If you do it is treated as a function call t0 is the time at which the initial condition occurs By def...

Page 430: ...1 ncurves 0 diftol 001 7 In the Home screen use BldData to create a data variable containing the RK graphing points 8 Return to the Y Editor press 9 or 8 Í Set Solution Method EULER Note You do not need to graph the equation before using BldData For more information about BldData refer to the Technical Reference module 9 Return to the Home screen and use BldData to create a data variable containin...

Page 431: ...as shown To define a column header move the cursor to that column press type the reference expression such as rklog 1 for c1 and press Note rklog 1 and rklog 2 refer to column 1 and 2 in rklog respectively Likewise with eulerlog 2 12 In the Data Matrix Editor press Then press and define Plot 1 for the RK data as shown to the right 13 Define Plot 2 for the Euler data Use the values shown to the rig...

Page 432: ...1 and Plot 2 16 In the Window Editor set the Window variables xmin L10 xmax 100 xscl 10 ymin L10 ymax 120 yscl 10 xres 2 17 Display the Graph screen 8 Note The fuzzy line on the graph indicates differences between the RK and Euler values 18 In the Window Editor set the Window variables to zoom in so that you can examine the differences in more detail xmin 39 7 xmax 40 3 xscl 1 ymin 85 5 ymax 86 ys...

Page 433: ...lot 2 is 85 6527 You can also use the Data Matrix Editor to open the errorlog data variable and scroll to time 40 Example of the deSolve Function The deSolve function lets you solve many 1st and 2nd order ordinary differential equations exactly 20 Press to trace and then press C or D until y1 is selected 1 shows in upper right corner Then enter 40 RK Plot 1 Euler Plot 2 Exact solution y1 y1 is sel...

Page 434: ...stic 1st order differential equation find the general solution for y with respect to t Notes For maximum accuracy use 1 1000 instead of 001 A floating point number can introduce round off errors This example does not involve graphing so you can use any Graph mode deSolve y 1 1000 yù 100Ny t y Do not use implied multiplication between the variable and parentheses If you do it will be treated as a f...

Page 435: ...hlight the solution in the history area Then press to autopaste it into the entry line b Insert the Define instruction at the beginning of the line Then press Note Press 2 A to move to the beginning of the entry line 3 For an initial condition y 10 with t 0 use solve to find the 1 constant Note If you got a different constant 2 etc solve for that constant 1 represents a constant You may get a diff...

Page 436: ...tial equation this section can help you correct the problem Many problems may be related to your Fields graph format setting Setting the Fields Graph Format What Order Equation Are You Graphing 4 Evaluate the general solution y with the constant 1 9 100 to obtain the particular solution shown From the Y Editor Window Editor or Graph screen press 9 or 8 Í If the equation is Valid Fields settings ar...

Page 437: ...pplicable setting For a particular Fields setting check the following for information that applies to that setting 2nd order system of two 1st order equations DIRFLD or FLDOFF 3rd or higher order system of three or more 1st order equations FLDOFF Because Fields SLPFLD is the default setting a common error message is shown to the right If the equation is Valid Fields settings are ...

Page 438: ...n enter mulNotele equations but only one at a time can be selected The selected equation must not refer to any other equation in the Y Editor For example If y1 y2 an Undefined variable error occurs when you graph In the Graph screen If the slope field is drawn but no solution curve is plotted specify an initial condition ...

Page 439: ...raph If you enter initial conditions in the Y Editor the equations referenced by the custom axes must have the same number of initial conditions Otherwise a Dimension error occurs when you graph With custom axes Set axes that are valid for your system of equations Do not select t for either axis Otherwise an Invalid axes error occurs when you graph The two axes must refer to different equations in...

Page 440: ...IRFLD the equations referenced by the custom axes determine which equations are graphed regardless of which equations are selected in the Y Editor If your system of equations refers to t the direction field not the plotted curves is drawn with respect to one particular time which is set by the dtime Window variable In the Y Editor If you enter a 2nd or higher order equation enter it as a valid sys...

Page 441: ...tor whether the equation is selected or not Otherwise a Diff Eq setup error occurs when you graph In the Graph screen If no curve is graphed set an initial condition If you did enter initial conditions in the Y Editor select ZoomFit j A A 1st order equation may look different with FLDOFF than with SLPFLD This is because FLDOFF uses the tplot and tmax Window variables page 9 which are ignored with ...

Page 442: ...rating a Table 1 Set Graph mode and if necessary Angle mode 3 Note Tables are not available in 3D Graph mode 2 Define functions on Y Editor 8 3 Select which defined functions to display in the table Note For information on defining and selecting functions with the Y Editor refer to Basic Function Graphing 4 Set up the initial table parameters 8 Note You can specify an automatic table that is based...

Page 443: ... the independent variable you can zoom in or out on the table to see different levels of detail Change the cell width Edit selected functions Build or edit a manual table to show only specified values of the independent variable Setting Up the Table Parameters To set up the initial parameters for a table use the TABLE SETUP dialog box After the table is displayed you can also use this dialog box t...

Page 444: ...able tbl If Independent AUTO and Graph Table OFF this specifies the incremental value for the independent variable tbl can be positive or negative but not zero Graph Table If Independent AUTO OFF The table is based on the values you enter for tblStart and tbl ON The table is based on the same independent variable values that are used to graph the functions on the Graph screen These values depend o...

Page 445: ...ging the Setup Parameters From the TABLE SETUP dialog box Independent AUTO The TI 89 Titanium automatically generates a series of values for the independent variable based on tblStart tbl and Graph Table ASK Lets you build a table manually by entering specific values for the independent variable To generate tblStart tbl Graph Table Independent An automatic table Based on initial values value value...

Page 446: ...table s parameters from the Home screen or a program You can Store values directly to the system variables tblStart and tbl Refer to Storing and Recalling Variable Values in Operating the Calculator To change Do this tblStart or tbl Type the new value The existing value is erased when you start to type or Press A or B to remove the highlighting Then edit the existing value Graph Table or Independe...

Page 447: ... the trace values from the Graph screen If Graph Table OFF the table is based on the values you entered for tblStart and tbl Before You Begin Define and select the applicable functions on the Y Editor This example uses y1 x x3Nx 3 Displaying the Table Screen To display the Table screen press or O 5 The cursor initially highlights the cell that contains the starting value of the independent variabl...

Page 448: ... When you scroll right or left the values of the independent variable are always visible along the left side of the screen To move the cursor Press One cell at a time D C B or A One page at a time 2 and then D C B or A First column shows values of the independent variable Header row shows names of independent variable x and selected functions y1 Entry line shows full value of highlighted cell Othe...

Page 449: ... cursor to highlight a number and press For single digit numbers you can type the number and press 4 Press to close the dialog box and update the table How Numbers Are Displayed in a Cell Whenever possible a number is shown according to the currently selected display modes Display Digits Exponential Format etc The number may be rounded as necessary However To change the cell width from the Table s...

Page 450: ... setting a number is shown with up to six digits even if the cell is wide enough to show more Other settings similarly affect a displayed number Note To see a number in full precision highlight the cell and look at the entry line If cell width is Full Precision 3 6 9 12 1 2345678901 1 2 1 2346 1 23457 1 23457 L123456 78 L1 2E5 L123457 L123457 000005 5 EL6 000005 000005 1 2345678E19 1 2E19 1 2346E1...

Page 451: ...aving to use the Y Editor 1 Move the cursor to any cell in the column for that function The table s header row shows the function names y1 etc 2 Press to move the cursor to the entry line where the function is displayed and highlighted Note You can use this feature to view a function without leaving the table 3 Make any changes as necessary Type the new function The old function is erased when you...

Page 452: ...e TABLE SETUP dialog box Then make your changes Building a Manual Ask Table If Independent ASK on the TABLE SETUP dialog box the TI 89 Titanium lets you build a table manually by entering specific values for the independent variable Displaying the Table Screen To display the Table screen press If you set Independent ASK with before displaying a table for the first time a blank table is displayed T...

Page 453: ...a blank table you can enter a value in consecutive cells only row 1 row 2 etc You cannot skip cells row 1 row 3 If a cell in column 1 contains a value you can edit that value 2 Press to move the cursor to the entry line 3 Type a new value or expression or edit the existing value 4 Press to move the value to the table and update the corresponding function values Note To enter a new value in a cell ...

Page 454: ...ries of values enclosed in braces and separated by commas For example You can also enter a list variable or an expression that evaluates to a list Note If the independent variable column contains existing values they are shown as a list which you can edit 4 Press to move the values into the independent variable column The table is updated to show the corresponding function values Enter values in a...

Page 455: ...ependent variable values that are currently displayed Before displaying a table you can store a list of values directly to the tbl nput system variable To Do this Insert a new row above a specified row Highlight a cell in the specified row and press 2 ˆ The new row is undefined undef until you enter a value for the independent variable Delete a row Highlight a cell in the row and press If you high...

Page 456: ...Tables 453 ...

Page 457: ...ystem data variable that can be opened in the Data Matrix Editor Collecting the Points 1 Display the graph This example shows y1 x 5ùcos x 2 Display the coordinates or math results you want to collect 3 Save the information to the Home screen or the sysData variable 8 Home screen or 8 b sysData variable 4 Repeat the process as necessary Note To display coordinates or math results trace a function ...

Page 458: ...any existing data Existing titles or column headers for the affected columns are cleared titles are replaced with the applicable titles for the new data The sysData variable can be cleared deleted etc just as any other data variable However it cannot be locked 8 b 8 Displayed coordinates are added to the Home screen s history area but not the entry line as a single row matrix or vector Displayed c...

Page 459: ...nction or expression on the Home screen and then decide to graph it You can copy an expression to the Y Editor or graph it directly from the Home screen without using the Y Editor What Is the Native Independent Variable On the Y Editor all functions must be defined in terms of the current graph mode s native independent variable Graph Mode Native Independent Variable Function x Parametric t Polar ...

Page 460: ... the desired function and press 3 Press ƒ and select 6 Paste Then press Note Instead of using ƒ 5 or ƒ 6 to copy and paste use 8 6 or 8 7 Store the expression to a Y function name Note To copy an expression from the Home screen s history area to the entry line use the auto paste feature or copy and paste Define command Define the expression as a user defined Y function Note Define is available fro...

Page 461: ...ired function and press 2 Press 2 Type the variable name that contains the expression and press twice Important To recall a function variable such as f1 x type only f1 not the full function name 3 Press to save the recalled expression in the Y Editor s function list Note 2 is useful if an expression is stored to a variable or function that does not correspond to the Y Editor such as a1 or f1 x If ...

Page 462: ...e Y Editor Instead it temporarily suspends any functions selected on the Y Editor You can trace zoom or show and edit Graph expressions on the Table screen just the same as Y Editor functions Clearing the Graph Screen Each time you execute Graph the new expression is added to the existing ones To clear the graphs A non native independent variable In PARAMETRIC graphing mode Graph xExpr yExpr t In ...

Page 463: ...ctions You can define a user defined function in terms of any independent variable For example and Graphing a Piecewise Defined Function To graph a piecewise function you must first define the function by specifying boundaries and expressions for each piece The when function is extremely useful for Define f1 aa 1 25aaùcos aa Graph f1 x Define f1 aa 1 25aa cos aa Refers to the function by using the...

Page 464: ...n Function To define a two piece function use the syntax when condition trueExpression falseExpression For example suppose you want to graph a function with two pieces For three or more pieces you can use nested when functions When Use expression x 0 Mx x 0 5 cos x In the Y Editor The function is pretty printed in this form Enter the function in this form ...

Page 465: ...and difficult to visualize Using a Multi Statement User Defined Function For three or more pieces you may want to create a multi statement user defined function When Use expression x Mp 4 sin x x M p and x 0 2x 6 x 0 6 x2 In the Y Editor y1 x when x 0 when x M p 4ùsin x 2x 6 6Nx 2 This nested function is in effect when x 0 ...

Page 466: ...uctures If ElseIf Return etc used in programming When creating the structure of a function it may be helpful to visualize it first in a block form Ê Func and EndFunc must begin and end the function When entering a multi statement function on the Y Editor or Home screen you must enter the entire function on a single line When Use expression x Mp 4 sin x x M p and x 0 2x 6 x 0 6 x2 Ê Ê Func If x M p...

Page 467: ...ion For example use the Program Editor to create a function named f1 xx In the Y Editor set y1 x f1 x Graphing a Family of Curves By entering a list in an expression you can plot a separate function for each value in the list You cannot graph a family of curves in SEQUENCE or 3D graphing mode In the Y Editor Func If x Mp Then Return 4ùsin x EndIf EndFunc Use a colon to separate each statement Only...

Page 468: ...d separate them with commas Enter the expression 2 4 6 sin 1 2 3 x and graph the functions Note The commas are shown in the entry line but not in the function list Example Using the Graph Command Similarly you can use the Graph command from the Home screen or a program Graphs three functions 2 sin x 4 sin x 6 sin x Graphs three functions 2 sin x 4 sin 2x 6 sin 3x ...

Page 469: ...are graphed sequentially Note To set graph formats from the Y Editor Window Editor or Graph screen press 8 Í When Tracing a Family of Curves Pressing D or C moves the trace cursor to the next or previous curve in the same family before moving to the next or previous selected function For these example functions the TI 89 Titanium Voyage 200 graphing calculator graphs three groups 2 sin x x 4 cos x...

Page 470: ...or more information about split screens refer to Split Screens Setting the Mode Several mode settings affect the two graph mode but only two settings are required Both are on Page 2 of the MODE dialog box 1 Press 3 Then press to display Page 2 3 Optionally you can set the following modes 2 Set the following required modes Split Screen TOP BOTTOM or LEFT RIGHT Number of Graphs 2 Page 1 Graph Graph ...

Page 471: ...ndent Graph modes FUNCTION POLAR etc Other modes such as Angle Display Digits etc are shared and affect both graphs Page 2 Split 1 App application for top or left side Split 2 App application for bottom or right side Graph 2 Graph mode for bottom or right side Graph 2 right or bottom side Graph mode of active graph Graph 1 left or top side Thick border indicates active graph side Active graph side...

Page 472: ...lications Y Editor Graph screen etc can be displayed on both sides of the screen at the same time Non graph related applications Home screen Data Matrix Editor etc are shared and can be displayed on only one side at a time The Y Editor in Two Graph Mode Even in two graph mode there is actually only one Y Editor which maintains a single function list for each Graph mode setting However if both side...

Page 473: ... complete information about split screens refer to Split Screens To switch from one graph side to the other press 2 a second function of O To display different applications Switch to the applicable graph side and display the application as you normally would or Use 3 to change Split 1 App and or Split 2 App To exit two graph mode When both sides use the same graphing mode each side shows the same ...

Page 474: ...een on only one side at a time Remember that the Two Sides Are Independent In two graph mode the two sides may appear to be related when in fact they are not For example After the two graph mode is set up graph related operations refer to the active graph side For example affects either Graph 1 or Graph 2 depending on which is active when you execute the command For Graph 2 the polar graph uses r ...

Page 475: ...ion of the graph You can also draw the inverse of a function These operations are not available for 3D graphs Drawing a Function Parametric or Polar Equation Execute DrawFunc DrawParm or DrawPol from the Home screen or a program You cannot draw a function or equation interactively from the Graph screen DrawFunc expression DrawParm expression1 expression2 tmin tmax tstep DrawPol expression qmin qma...

Page 476: ... the graph of y1 x 1x3 2x 6 as shown above 2 On the Graph screen press 2 ˆ and select 2 DrawFunc To display the Home screen and put DrawFunc in the entry line press 2 ˆ 2 3 On the Home screen specify the function to draw 4 Press to draw the function on the Graph screen You cannot trace zoom or perform a math operation on a drawn function Note To clear the drawn function press or 2 ˆ and select 1 C...

Page 477: ...n the Graph screen usually for comparisons For example draw a horizontal line to show that two parts of a graph have the same y value Some objects are not available for 3D graphs Clearing All Drawings A drawn object is not part of the graph itself It is drawn on top of the graph and remains on the screen until you clear it 2 On the Home screen specify the inverse function 3 Press The inverse is pl...

Page 478: ...You can also enter ClrDraw on the Home screen s entry line You can also do anything that causes the Smart Graph feature to redraw the graph such as change the Window variables or deselect a function on the Y Editor 2 ˆ and select 1 ClrDraw or Press to regraph ...

Page 479: ...lack point or line If you start on a black pixel the pencil draws a white point or line which can act as an eraser 1 2 and select 1 Pencil 2 Move the cursor to the applicable location To draw a Do this Point pixel sized Press Freehand line Press and hold and move the cursor to draw the line After drawing the point or line you are still in Pencil mode To continue drawing move the cursor to another ...

Page 480: ...cable location Note These techniques also erase parts of graphed functions Drawing a Line Between Two Points From the Graph screen 1 2 and select 3 Line To erase Do this Area under the box Press Along a freehand line Press and hold and move the cursor to erase the line After erasing you are still in Eraser mode To continue erasing move the box cursor to another location To quit press N ...

Page 481: ... cursor in larger increments 2 B etc Drawing a Circle From the Graph screen 1 2 and select 4 Circle Note Use 2 to move the cursor in larger increments 2 B etc After drawing the line you are still in Line mode To continue drawing another line move the cursor to a new 1st point To quit press N 2 Move the cursor to the center of the circle and press 3 Move the cursor to set the radius and press ...

Page 482: ...n axis it may be difficult to see However you can easily see the flashing cursor 2 Use the cursor pad to move the line to the appropriate position Then press Note Use 2 to move the cursor in larger increments 2 B etc Drawing a Tangent Line To draw a tangent line use the Math toolbar menu From the Graph screen 1 Press and select A Tangent After drawing the line you are still in line mode To continu...

Page 483: ...execute the DrawSlp command from the Home screen or a program Use the syntax DrawSlp x y slope You can also access DrawSlp from the Graph screen 1 2 ˆ and select 6 DrawSlp This switches to the Home screen and puts DrawSlp in the entry line 3 Move the cursor to the tangent point and press The tangent line is drawn and its equation is displayed 2 Complete the command and press The calculator automat...

Page 484: ...e Screen or a Program Commands are available for drawing any of the objects described in this section There are also commands such as PxlOn PxlLine etc that let you draw objects by specifying exact pixel locations on the screen For a list of the available drawing commands refer to Drawing on the Graph Screen in Programming 3 Type the text label After typing the text you are still in text mode To c...

Page 485: ...ture of the Whole Graph Screen A picture includes any plotted functions axes tick marks and drawn objects The picture does not include lower and upper bound indicators prompts or cursor coordinates Display the Graph screen as you want to save it and then 1 Press ƒ and select 2 Save Copy As 2 Specify the type Picture folder and a unique variable name 3 Press After typing in an input box such as Var...

Page 486: ...You cannot save a portion of a 3D graph 2 Set the 1st corner of the box by moving its top and left sides Then press Note Use D and C to move the top or bottom and use B and A to move the sides 3 Set the 2nd corner by moving the bottom and right sides Then press 4 Specify the folder and a unique variable name 5 Press After typing in an input box such as Variable you must press twice Note When savin...

Page 487: ... Portion of the Graph Screen When you press ƒ and select 1 Open the picture is superimposed starting at the upper left corner of the Graph screen If the picture was saved from a portion of the Graph screen it may appear shifted from the underlying graph You can specify which screen pixel to use as the upper left corner 2 Select the type Picture folder and variable that contain the graph picture yo...

Page 488: ...nical Reference module To display a series of graph pictures as an animation use the CyclePic command For an example refer to CyclePic Command Animating a Series of Graph Pictures As described earlier in this module you can save a picture of a graph By using the CyclePic command you can flip through a series of graph pictures to create an animation CyclePic Command Before using CyclePic you must h...

Page 489: ...ws of a 3D graph with each view rotated 10 further around the Z axis For information about each command refer to the CyclePic picNameString n wait cycles direction Ê base name of pictures in quotes such as pic Ë of pictures to cycle Ì seconds between Í of times to repeat cycle Ê Ë Ì Í Î ...

Page 490: ...y Other Graph from Program cyc Prgm local I Set mode and Window variables setMode graph 3d 70 eyef M10 xmin 10 xmax 14 xgrid M10 ymin 10 ymax 14 ygrid M10 zmin 10 zmax 1 zscl Define the function x 3ùy y 3ùx 390 z1 x y Generate pics and rotate For i 1 10 1 iù10 eyeq DispG StoPic pic string i EndFor Display animation CyclePic pic 10 5 5 M1 EndPrgm ...

Page 491: ...elements that define a particular graph By saving a graph database as a GDB variable you can recreate that graph at a later time by opening its stored database variable Elements in a Graph Database A graph database consists of Mode settings 3 for Graph Angle Complex Format and Split Screen only if you are using the two graph mode All functions in the Y Editor 8 including display styles and which f...

Page 492: ...le screen or Graph screen Opening a Graph Database Caution When you open a graph database all information in the current database is replaced You may want to store the current graph database before opening a stored database 1 Press ƒ and select 2 Save Copy As 2 Specify the folder and a unique variable name 3 Press After typing in an input box such as Variable you must press twice Note If you start...

Page 493: ...en 2 described in Memory and Variable Management From a Program or the Home Screen You can save store and open recall a graph database by using the StoGDB and RclGDB commands as described in the Technical Reference module 1 Press ƒ and select 1 Open 2 Select the folder and variable that contain the graph database you want to open 3 Press Note If you start from the Graph screen be sure to use Type ...

Page 494: ...ou change it Setting the Split Screen Mode 1 Press 3 to display the MODE dialog box 2 Because the modes related to split screens are listed on the second page of the MODE dialog box either Use D to scroll down or Press to display Page 2 3 Set the Split Screen mode to either of the following settings For the procedure used to change a mode setting refer to Operating the Calculator Split Screen Sett...

Page 495: ...ode described in Additional Graphing Topics the same application can be in both parts of a split screen Before pressing to close the MODE dialog box you can use the Split 1 App and Split 2 App modes to select the applications you want to use Mode Specifies the application in the Split 1 App Top or left part of the split screen Split 2 App Bottom or right part of the split screen When you set Split...

Page 496: ...mmands refer to Drawing on the Graph Screen in Programming Due to the border that indicates the active application split screens have a smaller displayable area than a full screen TI 89 Titanium Mode Description Number of Graphs Note Leave this set to 1 unless you have read the applicable section in Additional Graphing Topics Lets you set up and display two independent sets of graphs This is an ad...

Page 497: ...A TOP BOTTOM 1 1 1 2 2 1 0 234 0 234 0 234 0 46 0 26 0 68 0 234 0 234 0 234 0 46 0 68 0 26 LEFT RIGHT 1 1 1 2 2 1 0 116 0 76 0 156 0 98 0 98 0 98 0 116 0 156 0 76 0 98 0 98 0 98 Method 1 Press 3 to display the MODE dialog box Then set Split Screen FULL When you press to close the dialog box the full sized screen shows the application specified in Split 1 App Split 1 App Split 2 App Split Ratio x y...

Page 498: ...he portions of the screen in which each App is displayed Note The Apps desktop always appears in the full screen view Method 2 Press 2 K twice to display a full sized Home screen If the calculator is turned off When you turn the calculator on again When you press 2 The split screen is still in effect but the Home screen is always displayed in place of the application that was active when you press...

Page 499: ... the bottom portion of the screen The highlighted numeral indicates the active portion of the split screen Left right split screen 1 indicates the application that will appear in the left portion of the screen 2 indicates the application that will appear in the right portion of the screen The highlighted numeral indicates the active portion of the split screen Names of open Apps Split screen indic...

Page 500: ... toolbar and status line which are always the full width of the display are associated with the active application For applications that have an entry line such as the Home screen and Y Editor the entry line is the full width of the display only when that application is active Switching between Applications Press 2 a second function of O to switch from one application to the other Toolbar is for Y...

Page 501: ...it screen Method 1 1 Use 2 a to switch to the application you want to replace 2 Use O or 8 such as 8 to select the new application Method 2 3 Press 3 and then 4 Change Split 1 App and or Split 2 App If you set Split 1 App and Split 2 App to the same application the calculator exits the split screen mode and displays the application full screen Toolbar is for Graph screen Thick border indicates the...

Page 502: ...active application For example If the Home screen Pressing 2 K Is not already displayed Opens the Home screen in place of the active application Is displayed but is not the active application Switches to the Home screen and makes it the active application Is the active application Exits the split screen mode and displays a full sized Home screen Entry line is for the active Y Editor not the Graph ...

Page 503: ...Split Screens 500 Note Both Top Bottom and Left Right splits use the same methods to select an application ...

Page 504: ...rings that may or may not be related Each item is called an element In the Data Matrix Editor a list variable If you enter more than one column of elements in a list variable it is converted automatically into a data variable Is shown as a single column of elements each in a separate cell Must be continuous blank or empty cells are not allowed within the list Can have up to 999 elements Ê Column t...

Page 505: ...may or may not be related In the Data Matrix Editor a data variable Although you must use commas to separate elements on the entry line spaces separate the elements in the history area To refer to a specified element in a list use the format shown to the right Ê Name of list variable Ë Element number or index number Can have up to 99 columns Can have up to 999 elements in each column Depending on ...

Page 506: ...ata variable to create Ë Names of existing list Although you cannot directly display a data variable on the Home screen you can display a specified column or element Ê Name of data variable Ë Column number Ì Column number Í Element number in the column For example Ê Displays column 1 of the variable data1 Ë Displays element 1 in column 1 of the variable data1 NewData data1 list1 list2 Ê Ë data1 1 ...

Page 507: ... refer to a specific element in a matrix For example enter mat1 2 1 to access the 1st element in the 2nd row Looks similar to a data variable but all columns must have the same length Is initially created with 0 in each cell You can then enter the applicable value in place of 0 From the Home screen or a program you can use 9 to store a matrix with either of the equivalent methods shown to the righ...

Page 508: ...en an existing variable Creating a New Data Matrix or List Variable 1 Press O and then select 2 Select 3 New 3 Specify the applicable information for the new variable Item Lets you Type Select the type of variable to create Press B to display a menu of available types Folder Select the folder in which the new variable will be stored Press B to display a menu of existing folders For information abo...

Page 509: ...or and go to another application at any time To return to the variable that was displayed when you left the Data Matrix Editor launch Data Matrix Editor again and select 1 Current Variable Type a new variable name If you specify a variable that already exists an error message will be displayed when you press When you press N or to acknowledge the error the NEW dialog box is redisplayed Row dimensi...

Page 510: ...ess ƒ and select 1 Open or From any application launch Data Matrix Editor again and select 2 Open Note Variable shows the first existing variable in alphabetic order If there are no existing variables nothing is displayed 1 Press ƒ and select 3 New 2 Specify the type folder and variable name For a matrix also specify the number of rows and columns 2 Select the type folder and variable to open 3 Pr...

Page 511: ... Matrix Editor is initially blank for a list or data variable or filled with zeros for a matrix If you open an existing variable the values in that variable are displayed You can then enter additional values or edit the existing ones The Data Matrix Editor Screen A blank Data Matrix Editor screen is shown below When the screen is displayed initially the cursor highlights the cell at row 1 column 1...

Page 512: ...dit the existing one 4 Press to enter the value into the highlighted cell When you press the cursor automatically moves to highlight the next cell so that you can continue entering or editing values However the variable type affects the direction that the cursor moves Note To enter a new value you can start typing without pressing or first However you must use or to edit an existing value Variable...

Page 513: ...alue in a cell the cursor moves to the next cell However you can move the cursor to any cell and enter a value If you leave gaps between cells your device handles the gaps automatically To move the cursor Press One cell at a time D C B or A One page at a time 2 and then D C B or A Go to row 1 in the current column or to the last row that contains data for any column on the screen respectively If t...

Page 514: ... column are handled the same as a list However if you leave a gap between columns that column is blank In a matrix variable when you enter a value in a cell outside the current boundaries additional rows and or columns are added automatically to the matrix to include the new cell Other cells in the new rows and or columns are filled with zeros Note Although you specify the size of a matrix when yo...

Page 515: ...number in full precision you can always highlight the cell and look at the entry line 2 With the current Cell Width setting highlighted press B or A to display a menu of digits 3 through 12 3 Move the cursor to highlight a number and press For single digit numbers you can type the number and press 4 Press to close the dialog box Cell width is the maximum number of characters that can be displayed ...

Page 516: ...e or a column in a data variable you can enter a function in the column header that automatically generates a list of elements In a data variable you can also define one column in terms of another Entering a Header Definition In the Data Matrix Editor To clear Do this A column 1 Move the cursor to any cell in the column 2 Press 2 ˆ and select 5 Clear Column This item is not available for a matrix ...

Page 517: ...ever if you want to edit the existing definition you must press To view an existing definition press or move the cursor to the header cell and look at the entry line 2 Type the new expression which replaces any existing definition If you used or in Step 1 the cursor moved to the entry line and highlighted the existing definition if any You can also Press M to clear the highlighted expression Then ...

Page 518: ...te For a data variable header definitions are saved when you leave the Data Matrix Editor For a list variable the definitions are not saved only their resulting cell values You can use an expression that For example Generates a series of numbers c1 seq x 2 x 1 5 c1 1 2 3 4 5 Refers to another column c2 2ùc1 c4 c1ùc2 sin c3 3 Press D or C to save the definition and update the columns Ê c1 seq x x 1...

Page 519: ... use those existing lists as columns in a data variable From the Do this Data Matrix Editor In the applicable column use to define the column header Refer to the existing list variable For example c1 list1 Home screen or a program Use the NewData command as described in the Technical Reference module For example Ê Data variable If this data variable already exists it will be redefined based on the...

Page 520: ...variables the Data Matrix Editor has an Auto calculate feature By default Auto calculate ON Therefore if you make a change that affects a header definition or any column referenced in a header definition all header definitions are recalculated automatically For example If you change a header definition the new definition is applied automatically If column 2 s header is defined as c2 2ùc1 any chang...

Page 521: ...r you can use the shift and cumSum functions as described below These descriptions differ slightly from the Technical Reference module This section describes how to use the functions in the Data Matrix Editor The Technical Reference module gives a more general description for the Home screen or a program Using the Shift Function The shift function copies a base column and shifts it up or down by a...

Page 522: ... To enter cumSum type it select it from the CATALOG or press 2 I and select it from the List submenu Ê Ë Ì Í Î Ê c2 shift c1 2 Ë c3 shift c1 M2 Ì Shifted columns have the same length as the base Í Last two elements of c1 shift down and out the bottom undefined elements shift into the top Î First two elements of c1 shift up and out the top undefined elements shift into the bottom cumSum column Colu...

Page 523: ...tical order You can also sort all columns as a whole based on a key column Sorting a Single Column In the Data Matrix Editor 1 Move the cursor to any cell in the column 2 Press 2 ˆ and select 3 Sort Column Numbers are sorted in ascending order Character strings are sorted in alphabetical order C1 C1 fred 75 sally 82 chris 98 jane chris 75 fred 98 jane 82 sally ...

Page 524: ...hen using this procedure for a data variable All columns must have the same length None of the columns can be locked defined by a function in the column header When the cursor is in a locked column Œ is shown at the beginning of the entry line 1 Move the cursor to any cell in the key column 2 In this example move the cursor to the second column c2 to sort by last name Note For a list variable this...

Page 525: ...le or you can select a column from a data variable and copy that column to a list Valid Copy Types Note A list is automatically converted to a data variable if you enter more than one column of information Procedure From the Data Matrix Editor 1 Display the variable that you want to copy You can copy a To a List List or data Data Data Data column List Matrix Matrix ...

Page 526: ... select the column that you want to copy 3 In the dialog box Select the Type and Folder for the copy Type a variable name for the copy When available select the column to copy from Note If you type the name of an existing variable its contents will be replaced Ê Column is dimmed unless you copy a data column to a list The column information is not used for other types of copies Ê List variable to ...

Page 527: ...Data Matrix Editor 524 ...

Page 528: ...ons refer to the following pages 1 Set Graph mode 3 to FUNCTION 2 Enter stat data in the Data Matrix Editor Note Refer to the Data Matrix Editor module for details on entering data in the Data Matrix Editor 3 Perform stat calculations to find stat variables or fit data to a model 4 Define and select stat plots and then Note You can also use the Y Editor to define and select stat plots and y x func...

Page 529: ...lations You can analyze one variable or two variable statistics or perform several types of regression analyses The Calculate Dialog Box You must have a data variable opened The Data Matrix Editor will not perform statistical calculations with a list or matrix variable 6 Change the graph format if necessary 7 9 or 8 Í Graph the selected equations 8 ...

Page 530: ...xample shows all items as active On your calculator items are active only if they are valid for the current settings of Calculation Type and Freq and Categories Note If an item is not valid for the current settings it will appear dimmed You cannot move the cursor to a dimmed item Pathname of the data variable ...

Page 531: ...u store the regression equation so that it will be displayed in the Y Editor Use Freq and Categories Select NO or YES Note that Freq Category and Include Categories are active only when Use Freq and Categories YES Freq Type the column number that contains a weight value for each data point If you do not enter a column number all data points are assumed to have the same weight 1 Category Type the c...

Page 532: ...ayed on the STAT VARS screen The format depends on the Calculation Type For example Note Any undefined data points shown as undef are ignored in a stat calculation 4 To close the STAT VARS screen press Redisplaying the STAT VARS Screen The Data Matrix Editor s Stat toolbar menu redisplays the previous calculation results until they are cleared from memory 2 For Calculation Type OneVar For Calculat...

Page 533: ...ata variable Results are also cleared if you leave and then reopen the Data Matrix Editor with a data variable Change the current folder if the calculation referred to a list variable in the previous folder Statistical Calculation Types As described in the previous section the Calculate dialog box lets you specify the statistical calculation you want to perform This section gives more information ...

Page 534: ...ariable statistics Calculates the statistical variables CubicReg Cubic regression Fits the data to the third order polynomial y ax3 bx2 cx d You must have at least four data points For four points the equation is a polynomial fit For five or more points it is a polynomial regression ExpReg Exponential regression Fits the data to the model equation y abx where a is the y intercept using a least squ...

Page 535: ...o the model y ax b where a is the slope and b is the y intercept using the median median line which is part of the resistant line technique Summary points medx1 medy1 medx2 medy2 medx3 and medy3 are calculated and stored to variables but they are not displayed on the STAT VARS screen PowerReg Power regression Fits the data to the model equation y axb using a least squares fit and transformed value...

Page 536: ...lly display the results Use the ShowStat command to show the calculation results Statistical Variables Statistical calculation results are stored to variables To access these variables type the variable name or use the VAR LINK screen as described in Memory and Variable QuartReg Quartic regression Fits the data to the fourth order polynomial y ax4 bx3 cx2 dx e You must have at least five data poin...

Page 537: ... However regCoef and regeq are treated as a list and a function variable respectively One Var Two Var Regressions mean of x values ü ü sum of x values Gx Gx sum of x2 values Gx2 Gx2 sample std deviation of x Sx Sx population std deviation of x sx sx number of data points nStat nStat mean of y values ÿ sum of y values Gy sum of y2 values Gy2 sample standard deviation of y Sy population std deviatio...

Page 538: ...s 4 7 To access the a coefficient the 1st element in the list use an index such as regCoef 1 maximum of x values maxX maxX minimum of y values minY maximum of y values maxY 1st quartile q1 median medStat 3rd quartile q3 regression equation regeq regression coefficients a b c d e regCoef correlation coefficient corr coefficient of determination R2 summary points MedMed only medx1 medy1 medx2 medy2 ...

Page 539: ... Procedure From the Data Matrix Editor 1 Press to display the Plot Setup screen Initially none of the plots are defined 2 Move the cursor to highlight the plot number that you want to define 3 Press to define the plot This example shows all items as active On your calculator items are active only if they are valid for the current setting of Plot Type and use Freq and Categories Note If an item is ...

Page 540: ...width of each bar in a histogram Freq and Categories Select NO or YES Note that Freq Category and Include Categories are active only when Freq and Categories YES Freq is active only for Plot Type Box Plot or Histogram Freq Type the column number that contains a weight value for each data point If you do not enter a column number all data points are assumed to have the same weight 1 Category Type t...

Page 541: ...ories is available 5 Press after typing in an input box press twice Note Any undefined data points shown as undef are ignored in a stat plot Selecting or Deselecting a Plot From Plot Setup highlight the plot and press to toggle it on or off If a stat plot is selected it remains selected when you Change the graph mode Stat plots are not graphed in 3D mode The Plot Setup screen is redisplayed The pl...

Page 542: ...press To redefine an existing plot you do not necessarily need to clear it first you can make changes to the existing definition To prevent a plot from graphing you can deselect it Statistical Plot Types When you define a plot as described in the previous section the Plot Setup screen lets you select the plot type This section gives more information about the available plot types 1 Highlight the p...

Page 543: ... same length Xyline Plotted points are shown with the symbol that you select as the Mark If necessary you can specify the same column or list for both x and y This is a scatter plot in which data points are plotted and connected in the order in which they appear in x and y You may want to sort all the columns in the Data Matrix Editor before plotting 2 ˆ 3 or 2 ˆ 4 ...

Page 544: ...istical data as a modified box plot Select Mod Box Plot as the Plot Type when you define a plot in the Data Matrix Editor A modified box plot excludes points outside the interval Q1NX Q3 X where X is defined as 1 5 Q3NQ1 These points called outliers are plotted individually beyond the box plot s whiskers using the mark that you select A box is defined by its first quartile Q1 median Med and third ...

Page 545: ...rom the Graph screen Y Editor or Window Editor adjusts xmin and xmax to include all data points but it does not adjust the y axis Use 8 to set ymin 0 and ymax the number of data points expected in the tallest bar When defining the plot you can specify the Hist Bucket Width default is 1 to set the width of each bar A data point at the edge of a bar is counted in the bar to the right xmin Hist Bucke...

Page 546: ...ons described how to define and select stat plots from the Data Matrix Editor You can also define and select stat plots from the Y Editor When you trace a histogram the screen shows information about the traced bar Trace cursor Range of the traced bar of data points in the traced bar ...

Page 547: ...some information To see the list of stat plots use C to scroll above the y x functions From the Y Editor you can perform most of the same operations on a stat plot as you can on any other y x function For example PLOTS 23 means that Plots 2 3 are selected If a Plot is highlighted this shows the data variable that will be used for the plots If a Plot is defined it shows the same shorthand notation ...

Page 548: ... x functions at the same time Graphing and Tracing a Defined Stat Plot After entering the data points and defining the stat plots you can graph the selected plots by using the same methods you used to graph a function from the Y Editor as described in Basic Function Graphing To Do this Edit a plot definition Highlight the plot and press You will see the same definition screen that is displayed in ...

Page 549: ... Enter appropriate values or Select 9 ZoomData from the Zoom toolbar menu Although you can use any zoom ZoomData is optimized for st plots Note Zoom is available on the Y Editor Window Editor and Graph screen ZoomData sets the viewing window to display all statistical data points For histograms and box plots only xmin and xmax are adjusted If the top of a histogram is not shown trace the histogram...

Page 550: ...he left or right side of the screen However you can still press to center the screen on the trace cursor Press 9 or 8 Í from the Y Editor Window Editor or Graph screen Then change the settings as necessary Plot Type Description Scatter or xyline Tracing begins at the first data point Box plot Tracing begins at the median Press A to trace to Q1 and minX Press B to trace to Q3 and maxX Histogram The...

Page 551: ...gory values let you analyze a subset of the data points Example of a Frequency Column In a data variable you can use any column in the Data Matrix Editor to specify a frequency value or weight for the data points on each row A frequency value must be an integer 0 if Calculation Type OneVar or MedMed or if Plot Type Box Plot For other statistical calculations or plots the frequency value can be any...

Page 552: ...e of 0 effectively removes the data point from analysis To use frequency values specify the frequency column when you perform a statistical calculation or define a stat plot For example Test scores Frequency values c1 c2 These weighted scores are equivalent to the single column of scores listed to the right c1 85 1 85 97 1 97 92 2 92 Ê 89 1 92 Ê 91 1 89 95 3 91 95 Ë 95 Ë 95 Ë ...

Page 553: ...t to analyze the scores for the whole class but you also want to analyze categories such as 10th grade girls 10th grade boys 10th grade girls and boys etc First determine the category values you want to use Note You do not need a category value for the whole class Also you do not need category values for all 10th graders or all 11th graders since they are combinations of other categories Category ...

Page 554: ...e category values in two columns To use category values specify the category column and the category values to include in the analysis when you perform a statistical calculation or define a stat plot Test scores Category values c1 c2 85 1 97 3 92 2 88 3 90 2 95 1 79 4 68 2 92 4 84 3 82 1 ...

Page 555: ...o analyze Include Categories 10th grade girls 1 10th grade boys 2 10th grade girls and boys 1 2 11th grade girls 3 11th grade boys 4 11th grade girls and boys 3 4 all girls 10th and 11th 1 3 all boys 10th and 11th 2 4 Type the column number or list name that contains the category values Set this to YES Within braces type the category values to use separated by commas Do not type a column number or...

Page 556: ...I 89 Titanium by using the Get command which is described in the Technical Reference module Although each set of retrieved data can be stored in several variable types list real matrix pic using list variables makes it easier to perform statistical calculations When you transfer the collected information to the TI 89 Titanium you can specify the list variable names that you want to use For example...

Page 557: ...CBL 2 unit Referring to the CBL 2 Lists When you perform a statistical calculation or define a plot you can refer explicitly to the CBL 2 list variables For example Creating a Data Variable with the CBL 2 Lists You can create a new data variable that consists of the necessary CBL 2 list variables Type the CBL 2 list variable name instead of a column number ...

Page 558: ...refer to the Data Matrix Editor module At this point the columns are linked to the CBL 2 lists If the lists are changed the columns will be updated automatically However if the lists are deleted the data will be lost To make the data variable independent of the CBL 2 lists clear the column header for each column The information remains in the column but the column is no longer linked to the CBL 2 ...

Page 559: ...ta Plots 556 CBR You can also use the Calculator Based Ranger CBR to explore the mathematical and scientific relationships between distance velocity acceleration and time using data collected from activities you perform ...

Page 560: ...m I O screen in a dialog box or on the Graph screen Running a Program On the Home screen 1 Type the name of the program 3 Press 2 You must always type a set of parentheses after the name Some programs require you to pass an argument to the program Note Use 2 to list existing PRGM variables Highlight a variable and press to paste its name to the entry line prog1 If arguments are not required prog1 ...

Page 561: ...rogram execution if an error occurs press N You can then correct any problems and run the program again Note The TI 89 Titanium also checks for run time errors that are found within the program itself Breaking a Program When a program is running the BUSY indicator is displayed in the status line Do not enter after the program name This error message appears if you Do not enter enough arguments if ...

Page 562: ...h related commands typically use the Graph screen After the program stops the TI 89 Titanium shows the last screen that was displayed The Program I O Screen On the Program I O screen new output is displayed below any previous output which may have been displayed earlier in the same program or a different program After a full page of output the previous output scrolls off the top of the screen To d...

Page 563: ...ay output or to prompt the user for input You cannot perform calculations on this screen Note If Home screen calculations don t work after you run a program you may be on the Program I O screen Leaving the Program I O Screen From the Program I O screen Press to toggle between the Home screen and the Program I O screen or Press N 2 K or to display the Home screen or Display any other application sc...

Page 564: ...r function or start a new program or function Starting a New Program or Function 1 Press O and then select Program Editor 2 Select 3 New 3 Specify the applicable information for the new program or function Item Lets you Type Select whether to create a new program or function Folder Select the folder in which the new program or function will be stored For information about folders refer to the Calc...

Page 565: ...g a previous one Resuming the Current Program You can leave the Program Editor and go to another application at any time To return to the program or function that was displayed when you left the Program Editor launch Program Editor again and select 1 Current Variable Type a variable name for the program or function If you specify a variable that already exists an error message will be displayed wh...

Page 566: ... at any time 1 From within the Program Editor press ƒ and select 1 Open or From another application launch Program Editor again and select 2 Open Note By default Variable shows the first existing program or function in alphabetical order 1 Press ƒ and select 3 New 2 Specify the type folder and variable for the new program or function 3 Press twice 2 Select the applicable type folder and variable 3...

Page 567: ...ed automatically you can accumulate quite a few previous programs and functions which take up memory storage space To delete programs and functions use the VAR LINK screen 2 For information about VAR LINK refer to the Memory and Variable Management module Overview of Entering a Program A program is a series of commands executed in sequential order although some commands alter the program flow In g...

Page 568: ...d Editing Text in the Text Editor module After typing each program line press This inserts a new blank line and lets you continue entering another line A program line can be longer than one line on the screen if so it will wrap to the next screen line automatically Note Entering a command does not execute that command It is not executed until you run the program Entering Multi Command Lines To ent...

Page 569: ...se comments to enter information that is useful to someone reading the program code To enter the comment symbol press 8 d or Press and select 9 Controlling the Flow of a Program When you run a program the program lines are executed in sequential order However some commands alter the program flow For example Ê Ë prog1 Prgm Displays sum of 1 thru n Request Enter an integer n expr n n Convert to nume...

Page 570: ...mportant difference between performing a calculation on the Home screen and in a program For more complex programs that use If EndIf and loop structures such as For EndFor you can make the programs easier to read and understand by using indentation If x 5 Then Disp x is 5 Else Disp x is or 5 EndIf These calculations will not display a result in a program although they will on the Home screen 12ù6 ...

Page 571: ...put commands is available Displaying a calculation result does not store that result If you need to refer to a result later store it to a variable cos p 4 maximum Disp maximum Enter the values directly into the program itself Disp 12ù6 cos p 4 maximum Include input commands that prompt the users to enter the necessary values when they run the program Input Enter a value i Request Enter an integer ...

Page 572: ...ou cannot use circle as the program name because it conflicts with a command name Before drawing the circle the program turns off any selected Y Editor functions displays a standard viewing window and squares the window In the beside the program name specify the variables that will be used to store the passed values Notice that the program also contains commands that set up the Graph screen circ x...

Page 573: ...tions and instructions that you typically use from the Home screen Why Create a User Defined Function Functions as well as programs are ideal for repetitive calculations or tasks You only need to write the function once Then you can reuse it as many times as necessary Functions however have some advantages over programs The user must specify the applicable values as arguments within the The argume...

Page 574: ...generic functions that are not tied to specific variable names Note You can create a function from the Home screen but the Program Editor is more convenient for complex multi line functions Differences Between Functions and Programs This guidebook sometimes uses the word command as a generic reference to instructions and functions When writing a function however you must differentiate between inst...

Page 575: ...em as local from within the function Cannot call a program as a subroutine but it can call another user defined function Cannot define a program Cannot define a global function but it can define a local function Note Information about local variables is available Entering a Function When you create a new function in the Program Editor the TI 89 Titanium displays a blank template Note Use the curso...

Page 576: ...e are two ways to return a value from a function As the last line in the function before EndFunc calculate the value to be returned cube x Func x 3 EndFunc Function name which you specify when you create a new function Enter your commands between Func and EndFunc All function lines begin with a colon Be sure to edit this line to include any necessary arguments Remember to use argument names in the...

Page 577: ... local by using the Local command There is an implied Return at the end of the function If the last line is not an expression an error occurs Example of a Function The following function returns the xth root of a value y Two values must be passed to the function x and y Use Return This is useful for exiting a function and returning a value at some point other than the end of the function cube x Fu...

Page 578: ... another program as a subroutine The subroutine can be external a separate program or internal included in the main program Subroutines are useful when a program needs to repeat the same group of commands at several different places Function as called from the Home Screen Function as defined in the Program Editor 4ùxroot 3 125 20 xroot x y Func y 1 x EndFunc 3 x 125 y 5 ...

Page 579: ...lling an Internal Subroutine To define an internal subroutine use the Define command with Prgm EndPrgm Because a subroutine must be defined before it can be called it is a good practice to define subroutines at the beginning of the main program subtest1 Prgm For i 1 4 1 subtest2 i iù1000 EndFor EndPrgm subtest2 x y Prgm Disp x y EndPrgm ...

Page 580: ... commands Notes about Using Subroutines At the end of a subroutine execution returns to the calling program To exit a subroutine at any other time use the Return command A subroutine cannot access local variables declared in the calling program Likewise the calling program cannot access local variables declared in a subroutine Ê Ë Ë Ì subtest1 Prgm local subtest2 Define subtest2 x y Prgm Disp x y ...

Page 581: ...he variables affects how they are stored and accessed Scope of Variables Scope Description System Global Variables Variables with reserved names that are created automatically to store data about the state of the calculator For example Window variables xmin xmax ymin ymax etc are globally available from any folder You can always refer to these variables by using the variable name only regardless o...

Page 582: ...name For example 5 class start class Variable name start Folder Name After the program stops any folder variables created by the program still exist and still take up memory Local Variables Temporary variables that exist only while a program is running When the program stops local variables are deleted automatically To create a local variable in a program use the Local command to declare the varia...

Page 583: ... can specify an argument that includes the same variable that was used to define the function or create the program However to avoid Circular definition errors you must assign a value for x or i variables that are used in evaluating the function or running the program For example Ê Causes a Circular definition error message if x or i does not have a value The error does not occur if x or i has alr...

Page 584: ...utine or function variable within a program DelFold Deletes a folder All variables in that folder must be deleted first DelVar Deletes a variable getFold Returns the name of the current folder getType Returns a string that indicates the data type EXPR LIST etc of a variable Local Declares one or more variables as local variables Lock Locks a variable so that it cannot be accidentally changed or de...

Page 585: ...ogram is running Example of a Local Variable The following program segment shows a For EndFor loop which is discussed later in this module The variable i is the loop counter In most cases the variable i is used only while the program is running NewPic Creates a picture variable based on a matrix Rename Renames a variable Unarchiv Moves specified variables from user data archive memory to RAM Unloc...

Page 586: ...variable error message displays when you evaluate a user defined function or run a user defined program that references a local variable that is not initialized assigned a value This example is a multi statement function rather than a program Line breaks are shown here but you would type the text in the entry line as one continuous line such as Define fact n Func Local where the ellipsis indicates...

Page 587: ... a function or program to perform symbolic calculations you must use a global variable instead of a local However you must be certain that the global variable does not already exist outside of the program The following methods can help Refer to a global variable name typically with two or more characters that is not likely to exist outside of the function or program Include DelVar within the funct...

Page 588: ...ay information or prompt the user to perform some action For example Some input commands such as InputStr automatically store user input as a string and do not require the user to enter quotation marks A string cannot be evaluated mathematically even if it appears to be a numeric expression For example the string 61 represents the characters 6 and 1 not the number 61 Disp The result is answer or I...

Page 589: ...d dim Returns the number of characters in a string expr Converts a string into an expression and executes that expression This is the opposite of the string command Important Some user input commands store the entered value as a string Before you can perform a mathematical operation on that value you must convert it to a numeric expression format Returns an expression as a character string based o...

Page 590: ...n a string ord Returns the character code of the first character within a string This is the opposite of the char command right Returns a specified number of characters from the right side end of a string rotate Rotates the characters in a string The default is L1 rotate right one character shift Shifts the characters in a string and replaces them with spaces The default is L1 shift right one char...

Page 591: ...rs expressions lists or matrices but they must match in type and dimension Press 2 I and select 8 Test Then select the operator from the menu or Display the built in functions Press The test operators are listed near the bottom of the Built in menu Operator True if Example Greater than a 8 Less than a 0 Greater than or equal to a b 100 Less than or equal to a 6 b 1 Equal list1 list2 ƒ Not equal to...

Page 592: ...t function changes the result of a test from true to false and vice versa For example Note If you use not from the Home screen it is shown as in the history area For example not x 2 is shown as x 2 Operator True if Example and Both tests are true a 0 and a 10 or At least one test is true a 0 or b c 10 xor One test is true and the other is false a 6 b 1 xor c d not x 2 is true if is false if x 2 x ...

Page 593: ...om one place to another in a program F2 Control Toolbar Menu To enter If EndIf structures use the Program Editor s Control toolbar menu The If command is available directly from the menu To see a submenu that lists other If structures select 2 If Then When you select a structure such as If Then EndIf a template is inserted at the cursor location If Then Ê EndIf Ê The cursor is positioned so that y...

Page 594: ...must store a value to x before executing the If command Note Use indentation to make your programs easier to read and understand If Then EndIf Structures To execute one group of commands if a conditional test is true use the structure Ê Executed only if x 5 Ë Displays value of 2x if x 5 x if x 5 Ê Ë If x 5 Disp x is greater than 5 Disp x Ê Ê Ë If x 5 Then Disp x is greater than 5 2 x x EndIf Disp ...

Page 595: ...only if x 5 Ë Executed only if x 5 Ì Displays value of 2x if x 5 5x if x 5 If Then ElseIf EndIf Structures A more complex form of the If command lets you test a series of conditions Suppose your program prompts the user for a number that corresponds to one of four options To test for each option If Choice 1 If Choice 2 etc use the If Then ElseIf EndIf structure Ê Ê Ë Ë Ì If x 5 Then Disp x is grea...

Page 596: ...and Goto commands Use the Lbl command to label assign a name to a particular location in the program You can then use the Goto command at any point in the program to branch to the location that corresponds to the specified label Lbl labelName name to assign to this location use the same naming convention as a variable name Goto labelName specifies which Lbl command to branch to ...

Page 597: ...nclude commands such as Stop that prevent Lbl GT5 from being executed if x 5 Using Loops to Repeat a Group of Commands To repeat the same group of commands successively use a loop Several types of loops are available Each type gives you a different way to exit the loop based on a conditional test F2 Control Toolbar Menu Ê Ë If x 5 Goto GT5 Disp x Lbl GT5 Disp The number was 5 To enter most of the ...

Page 598: ... is Note The ending value can be less than the beginning value but the increment must be negative When you select a loop the loop command and its corresponding End command are inserted at the cursor location For Ê EndFor Ê If the loop requires arguments the cursor is positioned after the command For variable begin end increment Ê variable used as a counter Ë counter value used the first time For i...

Page 599: ...hat the program can exit the loop after a certain number of repetitions At the end of the loop EndFor program control jumps back to the For command where variable is incremented and compared to end For example Ê Displays 0 1 2 3 4 and 5 Ë Displays 6 When variable increments to 6 the loop is not executed Note You can declare the counter variable as local if it does not need to be saved after the pr...

Page 600: ...ommands that allow the program to exit the loop At the end of the loop EndWhile program control jumps back to the While command where condition is re evaluated To execute the loop the first time the condition must initially be true Any variables referenced in the condition must be set before the While command You can build the values into the program or prompt the user to enter the values The loop...

Page 601: ... Ì Increments x Í Displays 5 When x increments to 5 the loop is not executed Loop EndLoop Loops A Loop EndLoop creates an infinite loop which is repeated endlessly The Loop command does not have any arguments Ê Ë Ì Í 0 x While x 5 Disp x x 1 x EndWhile Disp x Loop EndLoop ...

Page 602: ...te The Exit command exits from the current loop In this example the If command can be anywhere in the loop The If command could also use a Goto command to transfer program control to a specified Lbl label command Ê Ë 0 x Loop Disp x x 1 x If x 5 Exit EndLoop Disp x When the If command is The loop is At the beginning of the loop Executed only if the condition is true At the end of the loop Executed...

Page 603: ...el and Goto commands are not strictly loop commands they can be used to create an infinite loop For example As with Loop EndLoop the loop should contain commands that let the program exit from the loop Configuring the TI 89 Titanium Programs can contain commands that change the configuration of the calculator Because mode changes are particularly useful the Program Editor s Mode toolbar menu makes...

Page 604: ...of calculator characteristics getFold Returns the name of the current folder getMode Returns the current setting for a specified mode getUnits Returns a list of default units setFold Sets the current folder setGraph Sets a specified graph format Coordinates Graph Order etc setMode Sets any mode except Current Folder setTable Sets a specified table setup parameter tblStart tbl etc setUnits Sets def...

Page 605: ...rogram can prompt the user to enter information while the program is running Likewise a program can display information such as the result of a calculation F3 I O Toolbar Menu 2 Press 2 ˆ to display a list of modes Note The Mode menu does not let you set the Current Folder mode To set this mode use the setFold command The correct syntax is inserted into your program setMode Graph FUNCTION To enter...

Page 606: ...reated as an expression An expression enclosed in quotes is treated as a string Input can also display the Graph screen and let the user update the variables xc and yc rc and qc in polar mode by positioning the graph cursor InputStr Prompts the user to enter an expression The expression is always treated as a string the user does not need to enclose the expression in quotes PopUp Displays a pop up...

Page 607: ...ent contents of the Program I O screen without displaying additional information DispG Displays the current contents of the Graph screen DispHome Displays the current contents of the Home screen DispTbl Displays the current contents of the Table screen Output Displays an expression or string starting at specified coordinates on the Program I O screen Format Formats the way in which numeric informa...

Page 608: ...consisting of Title Request etc commands that displays a dialog box Toolbar EndTbar Defines a program block consisting of Title Item etc commands that replaces the toolbar menus The redefined toolbar is in effect only while the program is running and only until the user selects an item Then the original toolbar is redisplayed CustmOn CustmOff Activates or removes a custom toolbar Custom EndCustm D...

Page 609: ...ture lets you create your own toolbar menu A custom menu can contain any available function instruction or set of characters The calculator has a default custom menu that you can modify or redefine DropDown Displays a drop down menu within a dialog box Item Displays a menu item for a redefined toolbar Request Creates an input box within a dialog box Text Displays a character string within a dialog...

Page 610: ...menu has been created the default custom menu is displayed To Do this Turn on the custom menu From the Home screen or any other application Press 2 From the Home screen or a program Execute the CustmOn command Turn off the custom menu From any application Press 2 again or Go to a different application Using the default custom menu on the Home screen 1 Select the Tools menu 2 Select 3 CustmOff This...

Page 611: ...the current cursor location For example Custom Title Vars Item L1 Item M1 Item Prgm1 Item Func1 Item Data1 Item Text1 Item Pic1 Item GDB1 Item Str1 Ê Title f x Ê Item f x Item g x Item f x y Item g x y Ê Item f x h Item Define f x Title Solve Item Solve Item and Item x y Item Solve and x y Custom Title title of F1 menu Item item 1 Item item 2 Title title of F2 menu Title title of F3 menu ...

Page 612: ...Item c Item u Title Tools Item ClrHome Item NewProb Item CustmOff EndCustm CustmOn Note The following may be slightly different than the default custom menu on your calculator Note See how _ o C and _ o F display as C and F in the menu Similarly see the international accented characters To modify the default custom menu use 3 Restore custom default as described below to get the commands for the de...

Page 613: ...ustom menu Then run the program for the menu you need Restoring the Default Custom Menu To restore the default 1 From the Home screen s normal menu not the custom menu select Clean Up 2 ˆ 3 Press to execute the commands and restore the default When you restore the default any previous custom menu is erased If the previous menu was created with a program you can run the program again if you want to...

Page 614: ...t table parameters To set the other two table parameters you can store the applicable values to the tblStart and tbl system variables Table Builds and displays a table based on one or more expressions or functions Command Description ClrGraph Erases any functions or expressions that were graphed with the Graph command Define Creates a user defined function DispG Displays the current contents of th...

Page 615: ...cts all or only specified stat data plots PlotsOn Selects all or only specified stat data plots setGraph Changes settings for the various graph formats Coordinates Graph Order etc setMode Sets the Graph mode as well as other modes Style Sets the display style for a function Trace Lets a program trace a graph ZoomBox to ZoomTrig Perform all of the Zoom operations that are available from the toolbar...

Page 616: ...series of stored graph pictures NewPic Creates a graph picture variable based on a matrix RclGDB Restores all settings stored in a graph database RclPic Displays the Graph screen and superimposes a stored graph picture by using OR logic RplcPic Clears the Graph screen and displays a stored graph picture StoGDB Stores the current graph settings to a graph database variable StoPic Copies the Graph s...

Page 617: ... in the Window Editor Note For information about pixel coordinates in split screens refer to the Data Matrix Editor module Many drawing commands have two forms one for pixel coordinates and one for point coordinates Note Pixel commands start with Pxl such as PxlChg Erasing Drawn Objects Pixel coordinates independent of viewing window Point coordinates for standard viewing window Command Descriptio...

Page 618: ...he pixel closest to the specified point PtOn or PxlOn Turns on displays a pixel at the specified coordinates PtOn which uses point coordinates affects the pixel closest to the specified point PtTest or PxlTest Returns true or false to indicate if the specified coordinate is on or off respectively PtText or PxlText Displays a character string at the specified coordinates Command Description Circle ...

Page 619: ...r PxlVert Draws erases or inverts a vertical line at a specified column coordinate Command Description DrawFunc Draws a specified expression DrawInv Draws the inverse of a specified expression DrawParm Draws a parametric equation using specified expressions as its x and y components DrawPol Draws a specified polar expression DrwCtour Draws contours in 3D graphing mode Shade Draws two expressions a...

Page 620: ... both units can transmit variables between them If you link a TI 89 Titanium to a Calculator Based Laboratory CBL 2 or a Calculator Based Ranger CBR a program on the TI 89 Titanium can access the CBL 2 or CBR F3 I O Toolbar Menu Use the Program Editor s I O toolbar menu to enter the commands in this section 1 Press and select 8 Link 2 Select a command ...

Page 621: ...th the CBL 2 or CBR unit Command Description GetCalc Executed on the receiving unit Sets up the unit to receive a variable via the I O port After the receiving unit executes GetCalc the sending unit must execute SendCalc After the sending unit executes SendCalc the sent variable is stored on the receiving unit in the variable name specified by GetCalc SendCalc Executed on the sending unit Sends a ...

Page 622: ...utomatically checks each executed command for syntax errors If there is an error a message indicates the nature of the error To cancel program execution and return to the Home screen press N If your program allows the user to select from several options be sure to run the program and test each option Send Sends a list variable from the graphing calculator to the CBL 2 or CBR To display the program...

Page 623: ... EndFunc to Prgm and EndPrgm Use Disp and Pause to debug the program Then remove Disp and Pause and change the program back into a function To confirm that a loop is executed the correct number of times display the counter variable or the values in the conditional test To confirm that a subroutine is executed display messages such as Entering subroutine and Exiting subroutine at the beginning and ...

Page 624: ... you can use to achieve the same goal Example 1 This example uses InputStr for input a While EndWhile loop to calculate the result and Text to display the result Ê Prompts for input on Program I O screen Ë Converts string entered with InputStr to an expression Ì Loop calculation Í Displays output in a dialog box Ê Ë Ì Ì Ì Ì Í prog1 Prgm InputStr Enter an integer n expr n n 0 temp 1 I While i n tem...

Page 625: ...ate a loop and Disp to display the result Ê Prompts for input on Program I O screen Ë Loop calculation Ì Displays output on Program I O screen Note Because Prompt returns n as a number you do not need to use expr to convert n Ê Ë Ë Ì prog2 Prgm Prompt n 0 temp 1 I Lbl top temp i temp i 1 I If i n Goto top Disp temp EndPrgm ...

Page 626: ... Ê Defines a dialog box for input Ë Converts string entered with Request to an expression Ì Loop calculation Í Defines a dialog box for output Ê Ê Ë Ì Ì Í Í ê prog3 Prgm Dialog Title Enter an integer Request Integer n EndDlog expr n n 0 temp 0 I Loop temp i temp i 1 I If i n Exit EndLoop Dialog Title The answer is Text string temp EndDlog EndPrgm ...

Page 627: ... do not need to use expr to convert n Ê Ë Ì prog4 Prgm Input Enter an integer n sum seq i i 1 n temp Disp temp EndPrgm Function Used in this example to seq Generate the sequence of integers from 1 to n sum Sum the integers in the list generated by seq seq expression var low high step Ê expression used to generate the sequence Ë variable that will be incremented Ì initial and final values of var Í ...

Page 628: ...de additional functions or features that are not built into the TI 89 Titanium Check the Texas Instruments web site for up to date information After downloading a program from the web to your computer use a USB cable or TI GRAPH LINK computer to calculator cable and TI Connect software to send the program to your TI 89 Titanium For Flash App installation instructions see education ti com guides No...

Page 629: ... type them within the Refer to the program s documentation to find out about required arguments If the program is not in the current folder be sure to specify the pathname You can call an assembly language program from another program as a subroutine delete it or use it the same as any other program Shortcuts to Run a Program On the Home screen you can use keyboard shortcuts to run up to nine user...

Page 630: ... an Assembly Language Program You cannot use your TI 89 Titanium to edit an assembly language program The built in Program Editor will not open assembly language programs Displaying a List of Assembly Language Programs To list the assembly language programs stored in memory 1 Display the VAR LINK screen 2 2 Press View Note Assembly language programs have an ASM data type 3 Select the applicable fo...

Page 631: ...an Exec command that executes a string consisting of a series of Motorola 68000 op codes These codes act as another form of an assembly language program Check the Texas Instruments web site for available information Note You must use a computer to write assembly language programs You cannot create assembly language programs from the calculator keyboard Warning Exec gives you access to the full pow...

Page 632: ...w Session 1 Press O and then select 2 Select 3 New The NEW dialog box is displayed 3 Specify a folder and text variable that you want to use to store the new session Item Description Type Automatically set as Text and cannot be changed Folder Shows the folder in which the text variable will be stored For information about folders refer to the Calculator Home Screen module To use a different folder...

Page 633: ... or opening a previous one Resuming the Current Session You can leave the Text Editor and go to another application at any time To return to the session that was displayed when you left the Text Editor launch Text Editor again and select 1 Current Variable Type a variable name If you specify a variable that already exists an error message will be displayed when you press When you press N or to ack...

Page 634: ...nd select 1 Open or From any application launch Text Editor again and select 2 Open Note By default Variable shows the first existing text variable in alphabetic order To leave the current Text Editor session and start a new one 1 Press ƒ and select 3 New 2 Specify a folder and text variable for the new session 3 Press twice 2 Select the applicable folder and text variable 3 Press ...

Page 635: ...ion Because all Text Editor sessions are saved automatically you can accumulate quite a few previous sessions which take up memory storage space To delete a session use the VAR LINK screen 2 to delete that session s text variable For information about VAR LINK refer to Memory and Variable Management Entering and Editing Text After beginning a Text Editor session you can enter and edit text In gene...

Page 636: ...s scroll off the top of the screen Using a USB cable and TI Connect software with the TI 89 Titanium you can use the computer keyboard to type a text file and then send that file to the TI 89 Titanium This is useful if you need to create a lengthy text file For information about obtaining cables or updated TI Connect software check the TI web site at education ti com or contact Texas Instruments a...

Page 637: ...he TI 89 Titanium alpha lock is always turned off when you change applications such as going from the Text Editor to the Home screen To Press Type a single lowercase alpha character j and then the letter key status line shows Type a single uppercase alpha character and then the letter key status line shows Type a space j alpha function of the key Turn on lowercase alpha lock 2 status line shows Tu...

Page 638: ...alpha lock off After you type the character alpha lock remains on Deleting Characters Note If there are no characters to the right of the cursor M erases the entire paragraph To delete Press The character to the left of the cursor 0 or 7 The character to the right of the cursor 8 same as 0 All characters to the right of the cursor through the end of the paragraph M All characters in the paragraph ...

Page 639: ...this Highlight text Move the cursor to the beginning or end of the text Hold and press A or B to highlight characters to the left or right of the cursor respectively D or C to highlight all characters up to the cursor position on the next or previous line respectively To Do this Replace highlighted text Type the new text Delete highlighted text Press 0 ...

Page 640: ...ress ƒ and then select 6 Paste You can use this general procedure to cut copy and paste text Within the same text session From one text session to another After cutting or copying text in one session open the other session and then paste the text From a text session to a different application For example you can paste the text into the Home screen s entry line 2 Press ƒ 3 Select the applicable men...

Page 641: ...the current cursor location 2 Press 3 Type the search text The search is not case sensitive For example CASE case and Case have the same effect Note The FIND dialog box retains the last search text you entered You can type over it or edit it 4 Press twice If the search text is The cursor Found Moves to beginning of the search text Not found Does not move ...

Page 642: ...press ƒ and then select 8 Clear Editor Entering Special Characters You can use the CHAR menu to select any special character from a list You can also type certain commonly used characters from the keyboard To see which characters are available from the keyboard you can display a map that shows the characters and their corresponding keys If the TI 89 Titanium is in The next character you type Will ...

Page 643: ... covers of this guidebook for a complete list of shortcut keys To access the shortcuts first press the 2 key Some special characters are marked on the keyboard but most are not On the TI 89 Titanium Press to display the keyboard map 1 Press 2 G 2 Select the applicable category A menu lists the characters in that category 3 Select a character You may need to scroll through the menu Note For accente...

Page 644: ...in this section SYSDATA b Copies the current graph coordinates to the system variable sysdata FMT Í Displays the FORMATS dialog box KBDPRGM1 9 1 through 9 If you have user defined or assembly language programs named kbdprgm1 through kbdprgm9 these shortcuts run the corresponding program OFF Similar to 2 except You can use if an error message is displayed When you turn the TI 89 Titanium on again i...

Page 645: ... only the special symbols On the TI 89 Titanium f Press and then the key for the symbol For example p times displays These special symbols are not affected by whether Alpha Lock is on or off Typing Greek Letters from the Keyboard Press the key combination that accesses the Greek character set on your calculator Then select the applicable alpha character on the keyboard to enter a Greek letter ...

Page 646: ...alculator does not display a map of Greek letters the map shown here is for reference only Several keys let you access lowercase and uppercase Greek letters For example On the TI 89 Titanium Press c to access the Greek character set Press c j letter to access lowercase Greek letters Example c j W displays ω A B C D E F G H I J K L M N O P Q R S U V W X Y Z T ψ ξ ζ τ α β δ ε φ γ Γ λ µ π Π ρ σ Σ ω Ω...

Page 647: ...alpha lock is on it turns alpha lock off For a List of All Special Characters For a list of all special characters refer to the Technical Reference module On the TI 89 Titanium if Then Alpha lock is off c X or c j X displays ξ j is not required for X Y Z or T c j W displays ω c 7 W displays Ω 7 is used for uppercase letters Lowercase alpha lock 2 is on c X displays ξ c W displays ω c 7 W displays ...

Page 648: ...ou can use the Text Editor to type a series of command lines that can be executed at any time on the Home screen This lets you create interactive example scripts in which you predefine a series of commands and then execute them individually Inserting a Command Mark In the Text Editor ...

Page 649: ...ed line 2 Press and select 4 Clear command 2 Press to display the Command toolbar menu 3 Select 1 Command C is displayed at the beginning of the text line to the left of the colon Note This does not insert a new line for the command it simply marks an existing line as a command line 4 Type a command just as you would on the Home screen The line can contain only the command with no additional text ...

Page 650: ...mporarily during execution and then the Text Editor is redisplayed After execution the cursor moves to the next line in the script so that you can continue to execute a series of commands Note To examine the result on the Home screen use a split screen or press Splitting the Text Editor Home Screen With a split screen you can view your command script and see the result of an executed command at th...

Page 651: ... Text Editor and the Home screen press 2 a second function of O Creating a Script from Your Home Screen Entries From the Home screen you can save all the entries in the history area to a text variable The entries are automatically saved in a script format so that you can open the text variable in the Text Editor and execute the entries as commands For information refer to Saving the Home Screen En...

Page 652: ...he command Note Some commands take longer to execute Wait until the Busy indicator disappears before pressing again 4 Continue using to execute each command but stop just before executing the Graph command 5 Execute the Graph command Note In this example the Graph command displays the Graph screen in place of the Home screen 6 Press and select 2 Clear split to return to a full screen Text Editor ...

Page 653: ... entering the equation that you want to solve Displaying the Numeric Solver Entering an Equation To display the Numeric Solver press O and then select The Numeric Solver screen shows the last entered equation if any On the eqn line type in your equation You can For example Type an equation directly a m2Nm1 m2 m1 g a b c sin d ...

Page 654: ... Solver you then would enter y1 x 0 or y1 t 0 etc Type an expression without an sign Note When you define the variables you can either define exp or solve for it e fNln g After you press the expression is set equal to a system variable called exp and entered as exp e fNln g Recall a previously entered equation or open a saved equation Note After you press the current equation is stored automatical...

Page 655: ...plays the most recently entered equation 2 Select an equation To select the displayed equation press To select a different equation press B to display a list Then select the one you want Note You can specify how many equations are retained From the Numeric Solver press and select 9 Format or use 8 Í Then select a number from 1 through 11 3 Press Only unique equations are listed If you re enter the...

Page 656: ...iable has an EXPR data type as shown on the MEMORY and VAR LINK screens Opening a Saved Equation To store the current equation for future use save it to a variable 1 From the Numeric Solver screen press and select 2 Save Copy As 2 Specify a folder and a variable name for the equation 3 Press twice To open a previously saved equation variable 1 From the Numeric Solver screen press and select 1 Open...

Page 657: ...e 3 Press After typing your equation on the eqn line press or D The screen lists the variables in the order they appear in the equation If a variable is already defined its value is shown You can edit these variable values Note If an existing variable is locked or archived you cannot edit its value Variable eqn contains the current equation it always appears alphabetically in the list The solution...

Page 658: ...ression it is evaluated when you move the cursor off the line The expression must evaluate to a real number If the equation contains a variable already defined in terms of other variables those other variables are listed Note When you assign a value to a variable in the Numeric Solver that variable is defined globally It still exists after you leave the solver Since a is defined in terms of g you ...

Page 659: ... not listed The solver uses the system variable s existing value Note You cannot solve for a system variable other than exp Also if the equation contains a system variable you cannot use to graph Although you can use a system variable in the equation an error occurs if you use to graph the solution If f a b was defined previously as a 2 b 2 and your equation contains f x y then x and y are listed ...

Page 660: ...tion if multiple solutions exist you can optionally If you see the error shown to the right delete the entered variable value Then edit the equation to use a different variable Note This error occurs if you use a reserved name incorrectly or refer to an undefined system function as a simple variable without parentheses Enter an initial guess for the unknown variable The guess must be within the sp...

Page 661: ... You can also select an initial guess graphically Solving for the Unknown Variable After you type an equation in the Numeric Solver and enter values for the known variables you are ready to solve for the unknown variable Finding the Solution With all known variables defined 1 Move the cursor to the unknown variable 2 Press Solve 3 A é marks the solution and leftNrt The édisappears when you edit a ...

Page 662: ...cannot converge on a solution this error occurs Graphing the Solution You can graph an equation s solutions any time after defining the known variables either before or after you solve for the unknown variable By graphing the solutions you can If you Do this Want to solve for other values Edit the equation or variable values Want to find a different solution for an equation with multiple solutions...

Page 663: ...r 4 ZoomFit The graph is shown in a split screen where The unknown variable is plotted on the x axis leftNrt is plotted on the y axis Solutions for the equation exist at leftNrt 0 where the graph crosses the x axis Note For more information refer to the Split Screens module Graph View uses the current Window variable values For information about ZoomStd and ZoomFit refer to Basic Function Graphing...

Page 664: ...se settings manually All stat plots are deselected After you leave the Numeric Solver the Graph screen may continue to display the equation s solution ignoring any selected Y functions If so display the Y Editor and then return to the Graph screen Also the graph is reset when you change the Graph mode or use ClrGraph from the Home screen 5 or a program Selecting a New Initial Guess from the Graph ...

Page 665: ...press and then select 2 Clear Graph View or To display the Home screen press 2 K twice 2 Use 2 a to make the Numeric Solver screen active 3 Make sure the cursor is on the unknown variable and press Note Cursor coordinate xc is the unknown variable value and yc is the leftNrt value 4 Press to re solve the equation sets the graph cursor s xc value as an initial guess and the yc value as leftNrt The ...

Page 666: ...ins single character variables their values may inadvertently affect later symbolic calculations Before leaving the Numeric Solver you may want to 1 Press 2 ˆ to clear all single character variables in the current folder 2 Press to confirm the action The screen returns to the solver s eqn line Note Any time you want to clear single character variables listed in the solver use 2 ˆ ...

Page 667: ... b or h in the prefix as well as hex characters A F in uppercase or lowercase If you enter a number without the 0b or 0h prefix such as 11 it is always treated as a decimal number If you omit the 0h prefix on a hexadecimal number containing A F all or part of the entry is treated as a variable 0b binaryNumber for example 0b11100110 Binary number with up to 32 digits Zero not the letter O and the l...

Page 668: ...rsions from the MATH Base menu For example to convert 256 from decimal to binary 256 4 Bin Note If your entry is not an integer a Domain error is displayed To convert 101110 from binary to hexadecimal 0b101110 4 Hex Instead of using 4 you can 1 Use 3 to set the Base mode to the base that you want to convert to For a binary or hex entry you must use the 0b or 0h prefix Results use the 0b or 0h pref...

Page 669: ...the Base mode However results are restricted to certain size limits when Base HEX or BIN Setting the Base Mode for Displayed Results 2 From the Home screen type the number that you want to convert using the correct prefix and press 1 Press 3 to display Page 2 of the MODE screen 2 Scroll to the Base mode press B and select the applicable setting 3 Press to close the MODE screen If Base mode HEX ...

Page 670: ... hex or binary number Fractional and floating point results are always shown in decimal form When Base HEX or BIN a division result is displayed in hexadecimal or binary form only if the result is an integer To ensure that division always produces an integer use intDiv instead of e If Base mode HEX 0h prefix in result identifies the base Press 8 to display the result in APPROXIMATE form If Base mo...

Page 671: ...00000 through 0hFFFFFFFF become negative numbers Comparing or Manipulating Bits The following operators and functions let you compare or manipulate bits in a binary number You can enter an integer in any number base Your entries are converted to binary automatically for the bitwise operation and results are displayed according to the Base mode Boolean Operations Operator with syntax Description no...

Page 672: ...omparison the result is 1 if either bit is 1 the result is 0 only if both bits are 0 The returned value represents the bit results integer1 xor integer2 In a bit by bit xor comparison the result is 1 if either bit but not both is 1 the result is 0 if both bits are 0 or both bits are 1 The returned value represents the bit results Suppose you enter 0h7AC36 and 0h3D5F Internally the hexadecimal inte...

Page 673: ... rotate integer ofRotations If ofRotations is omitted bits rotate once to the right default is L1 negative bits rotate the specified number of times to the right positive bits rotate the specified number of times to the left In a right rotation the rightmost bit rotates to the leftmost bit vice versa for a left rotation 0h7AC36 and 0h3D5F 0b00000000000001111010110000110110 and 0b000000000000000000...

Page 674: ...r of times to the left In a right shift the rightmost bit is dropped and 0 or 1 is inserted to match the leftmost bit In a left shift the leftmost bit is dropped and 0 is inserted as the rightmost bit Suppose you enter shift 0h7AC36 Internally the hexadecimal integer is converted to a signed 32 bit binary number Then the shift is applied to the binary number Function with syntax Description If Bas...

Page 675: ...be stored in a signed 32 bit binary form a symmetric modulo operation brings the value into the range 7AC36 0b00000000000001111010110000110110 Inserts 0 if leftmost bit is 0 or 1 if leftmost bit is 1 Dropped Each bit shifts to the right b00000000000000111101011000011011 0h3D61B Leading zeros are not shown in the result ...

Page 676: ...ess 2 The numbers on your MEMORY screen may vary from those shown Prgm Asn Includes programs written for the TI 89 Titanium as well as any assembly language programs you have loaded History Size of history pairs saved in the Home screen s history area FlashApp Size of Flash applications RAM free Free space in RAM Flash ROM free Free space in Flash ROM Note To display the size of individual variabl...

Page 677: ...m Description RAM 1 All RAM Resetting RAM erases all data and programs from RAM 2 Default Resets all system variables and modes to their original factory settings This does not affect any user defined variables functions or folders Flash ROM 1 Archive Resetting Archive erases all data and programs from Flash ROM 2 Flash Apps Resetting Flash Apps erases all Flash applications from Flash ROM 3 Both ...

Page 678: ...folders Displaying the VAR LINK Screen Press 2 By default the VAR LINK screen lists all user defined variables in all folders and with all data types Ê Folder names alphabetically listed Ë Shows installed Flash applications Ì Size in bytes Í Data type Î Variable names alphabetically listed This Indicates this 4 Collapsed folder view to right of folder name 6 Expanded folder view to right of folder...

Page 679: ...re are any variable names that start with that letter the cursor moves to highlight the first of those variable names Note Type a letter repeatedly to cycle through the names that start with that letter 6 You can scroll for more variables and or folders in bottom left corner of screen Ÿ If selected with Œ Locked û Archived This Indicates this ...

Page 680: ...NK screen and return to the current application use or N as described below Type Description ASM Assembly language program DATA Data EXPR Expression includes numeric values FUNC Function GDB Graph database LIST List MAT Matrix PIC Picture of a graph PRGM Program STR String TEXT Text Editor session Press To Paste the highlighted variable or folder name to the cursor location in the current applicat...

Page 681: ...iable You can show all variable types except ASM DATA GDB and variables created by Flash Apps For example you must open a DATA variable in the Data Matrix Editor 1 On VAR LINK move the cursor to highlight the variable 3 To return to VAR LINK press any key Note You cannot edit the contents from this screen N Return to the current application without pasting the highlighted name 2 Press 2 ˆ If you h...

Page 682: ... as the current folder all variables are stored in the To select Do this A single variable or folder Move the cursor to highlight the item then press A group of variables or folders Highlight each item and press A Ÿ is displayed to the left of each selected item If you select a folder all variables in that folder are selected Use to select or deselect an item All folders and all variables Press B ...

Page 683: ...te separate folders for different TI 89 Titanium applications Math Text Editor etc or classes You can store a user defined variable in any existing folder The user defined variables in one folder are independent of the variables in any other folder Therefore folders can store separate sets of variables with the same names but different values Example of variables that can be stored in MAIN only Wi...

Page 684: ...ccessible regardless of the current folder Note User defined variables are stored in the current folder unless you specify otherwise MAIN System variables User defined a 1 b 2 c 3 f x x x x ALG102 User defined b 5 c 100 f x sin x cos x DAVE User defined a 3 b 1 c 2 f x x 6 MATH User defined a 42 c 6 f x 3x 4x 25 Name of current folder Variables ...

Page 685: ...he current folder Creating a Folder from the Home Screen Enter the NewFold command on the Home screen Setting the Current Folder from the Home Screen Enter the setFold function on the Home screen 2 Press ƒ Manage and select 5 Create Folder Folder name to create This new folder is set automatically as the current folder NewFold folderName setFold is a function which requires you to enclose the fold...

Page 686: ...rresponding number or letter for that folder 5 Press to save your changes and close the dialog box Renaming Variables or Folders Remember if you use to select a folder the variables in that folder are selected automatically As necessary use to deselect individual variables 1 On VAR LINK select the variables and or folders 2 Highlight the Current Folder setting 3 Press B to display a menu of existi...

Page 687: ...a user defined variable or function that is not in the current folder Specify the complete pathname instead of only the variable name A pathname has the form folderName variableName or folderName functionName 3 Type a unique name and press twice If you selected multiple items you are prompted to enter a new name for each one ...

Page 688: ... variable name that is not in the current folder the pathname folderName variableName is pasted Listing Only a Specified Folder and or Variable Type or Flash application If you have a lot of variables folders or Flash applications it may be difficult to locate a particular variable By changing VAR LINK s view you can specify the information you want to see If Current Folder MAIN Folders and Variab...

Page 689: ...Highlight the setting you want to change and press B This displays a menu of valid choices To cancel a menu press N View Allows you to choose variables Flash applications or system variables to view Note To list system variables window variables etc select 3 System Folder Always lists 1 All and 2 main but lists other folders only if you have created them Var Type Lists the valid variable types ind...

Page 690: ...e to a different name in the same folder use 9 such as a1 a2 or the CopyVar command from the Home screen Locking or Unlocking Variables Folders or Flash Applications When a variable is locked you cannot delete rename or store to it However you can copy move or display its contents When a folder is locked you can manipulate the variables in the folder assuming the variables are not locked but you c...

Page 691: ...he variables in that folder are also deleted You cannot delete the MAIN folder Œ indicates a locked variable or folder in RAM û indicates an archived variable which is locked automatically 1 Press 2 2 Press to select the folder s to delete The folder s variables become selected automatically 3 Press ƒ 1 Delete or 0 4 Press to confirm the deletion of the folder and all its variables ...

Page 692: ...not delete the MAIN folder Pasting a Variable Name to an Application Suppose you are typing an expression on the Home screen and can t remember which variable to use You can display the VAR LINK screen select a variable from the list and paste that variable name directly onto the Home screen s entry line Which Applications Can You Use From the following applications you can paste a variable name t...

Page 693: ...asted 1 Position the cursor where you want to insert the variable name 2 Press 2 3 Highlight the applicable variable Note You can also highlight and paste folder names 4 Press to paste the variable name Note This pastes the variable s name not its contents Use 2 instead of 2 to recall a variable s contents 5 Finish typing the expression sin sin a1 sin a1 sin class a2 Assuming that CLASS is not the...

Page 694: ...nal free RAM by archiving variables For example You can archive variables that you need to access but do not need to edit or change or variables that you are not using currently but need to retain for future use Note You cannot archive variables with reserved names or system variables If you acquire additional programs for your TI 89 Titanium particularly if they are large you may need to create a...

Page 695: ...e For all purposes an archived variable is still in its original folder it is simply stored in the user data archive instead of RAM Note An archived variable is locked automatically You can access the variable but you cannot edit or delete it From the Home Screen or a Program Use the Archive and Unarchiv commands Archive variable1 variable2 Unarchiv variable1 variable2 3 Press ƒ and select either ...

Page 696: ...fter garbage collection depending on how much additional space is freed the variable may or may not be archived If not you can unarchive some variables and try again Why not Perform Garbage Collection Automatically without a Message The message Lets you know why an archive will take longer than usual It also alerts you that the archive may fail if there is not enough memory Can alert you when a pr...

Page 697: ...r Each variable that you archive is stored in the first empty block large enough to hold it Note An archived variable is stored in a continuous block within a single sector it cannot cross a sector boundary This process continues to the end of the last sector Depending on the size of individual variables the empty blocks may account for a significant amount of space Note Garbage collection occurs ...

Page 698: ...le it is copied to RAM but it is not actually deleted from user data archive memory Unarchived variables are marked for deletion meaning they will be deleted during the next garbage collection variable A variable D After you unarchive variables B and C they continue to take up space Sector 1 Sector 2 Sector 3 ...

Page 699: ...ion process Deletes unarchived variables from the user data archive Rearranges the remaining variables into consecutive blocks This TI 89 Titanium memory screen shows free space that will be available after all marked for deletion variables are deleted When you unarchive a variable the Flash ROM free amount increases immediately but the space is not actually available until after the next garbage ...

Page 700: ...hy does it matter how much RAM is available The answer is that the following operations can be performed only if a variable is in RAM Opening a text variable in the Text Editor Opening a data variable list or matrix in the Data Matrix Editor Opening a program or function in the Program Editor Running a program or referring to a function Note A temporary copy lets you open or execute an archived va...

Page 701: ... it is not copied if you perform 6ùab Correcting the Error To free up enough RAM to access the variable 1 Use the VAR LINK screen 2 to determine the size of the archived variable that you want to access 2 Use the MEMORY screen 2 to check the RAM free size 3 Free up the needed amount of memory by Deleting unnecessary variables from RAM Archiving large variables or programs moving them from RAM to t...

Page 702: ...t so you can connect TI graphing calculators with either type of link port However using the I O port requires the I O unit to unit cable sold separately or the USB Silver Edition cable also sold separately which is used to connect to a computer Connecting before Sending or Receiving Using firm pressure insert one end of the cable into the link port of each unit Either unit can send or receive dep...

Page 703: ...Connectivity 700 Two TI 89 Titanium calculators linked together Position so that the USB symbols face each other then insert the connector USB Port USB unit to unit cable USB Port USB unit to unit cable ...

Page 704: ...Connectivity 701 A TI 89 Titanium and a Voyage 200 linked together I O Port I O Port I O unit to unit cable ...

Page 705: ...itting Variables Flash Applications and Folders Transmitting variables is a convenient way to share any variable listed on the VAR LINK screen functions programs etc You can also transmit Flash applications Apps and folders TI 89 I O Port I O Port I O unit to unit cable ...

Page 706: ...cate Rules for Transmitting Variables Flash Applications or Folders Unlocked and unarchived variables that have the same name on both the sending and receiving units will be overwritten from the sending unit Locked variables that have the same name on both the sending and receiving units must be unlocked on the receiving unit before they can be overwritten from the sending unit If archived variabl...

Page 707: ...ed It remains unlocked on the receiving unit Locked Flash application If the receiving unit has the correct certification the Flash application is transmitted It remains locked on the receiving unit Unlocked Folder The folder and its selected contents are transmitted The folder remains unlocked on the receiving unit Locked Folder The folder and its selected contents are transmitted The folder beco...

Page 708: ... or A receiving unit is not attached to the other end of the cable or The receiving unit is not set up to receive Press N or to cancel the transmission Note The sending unit may not always display this message Instead it may remain BUSY until you cancel the transmission Sending unit The receiving unit does not have the correct certification for the operating system OS or Flash application being se...

Page 709: ...re the variable to a different name set Overwrite NO In the New Name input box type a variable name that does not exist in the receiving unit Then press twice To skip this variable and continue with the next one set Overwrite SKIP and press To cancel the transmission press N Receiving unit The receiving unit does not have enough memory for what is being sent Press N or to cancel the transmission S...

Page 710: ...e the Main folder To select multiple variables Flash applications or folders highlight each one and press to place a checkmark Ÿ beside it Use again to deselect any that you do not want to transmit To select all variables Flash applications or folders use All 1 Select All 3 Press ƒ and choose 1 Delete or Press 0 A confirmation message appears 4 Press to confirm the deletion Where to Get Flash Appl...

Page 711: ...ariable to the link port where a linked device can receive the variable The linked device must be on the Home screen or must execute GetCalc from a program You can use optional parameters with the SendCalc or GetCalc command to specify either the USB port or I O port See Appendix A for details If you do not include these parameters the TI 89 Titanium communicates through the USB port The Chat Prog...

Page 712: ...r enter a message in msg and send it Î Then sets up this unit to receive and display msg Ï Loop executed by the unit that sends the first message Chat Prgm ClrIO Disp On first unit to send enter 1 On first to receive InputStr enter 0 msg If msg 0 Then While true GetCalc msg Disp msg InputStr msg SendCalc msg EndWhile Else While true InputStr msg SendCalc msg GetCalc msg Disp msg EndWhile EndIf End...

Page 713: ...ices Use each device s Program Editor to enter the program or Enter the program on one device and then use VAR LINK to transmit the program variable to the other device To run the program on both devices 1 On the Home screen of each device enter chat 2 When each device displays its initial prompt respond as shown below 3 Take turns typing a message and pressing to send the variable msg to the othe...

Page 714: ... all user defined variables in both RAM and the user data archive functions programs lists and folders except the Main folder will be deleted It is possible that Flash applications could also be deleted You should use TI Connect software to back up your data to your computer before installing a new OS on your calculator See the important information concerning batteries before performing an OS upg...

Page 715: ...riables and modes to their original factory settings This is equivalent to using the MEMORY screen to reset all memory To retain any existing variables or Flash applications do the following before installing the upgrade Important Install new batteries Transmit the variables or Flash applications to another device or Use a USB cable or TI Connectivity Cable USB and TI Connect software education ti...

Page 716: ... transfer the Operating System OS from unit to unit 1 Link two like units together for example a TI 89 Titanium to a TI 89 Titanium or a Voyage 200 to a Voyage 200 2 On the receiving and the sending unit press 2 to display the VAR LINK screen 3 On the receiving and the sending unit press Link to display the menu options 4 On the receiving unit select 5 Receive OS A warning message displays Press N...

Page 717: ...contrast Do Not Attempt to Cancel an Operating System Transfer After the transfer starts the receiving unit s existing OS is effectively deleted If you interrupt the transfer before it is complete the receiving unit will not operate properly You will then need to reinstall the OS upgrade If You are Upgrading the Operating System on Multiple Units To perform an OS upgrade on multiple units download...

Page 718: ... The certificate on the receiving unit is not valid for the operating system OS or App on the sending unit You must obtain and install a valid certificate If the App no longer requires a certificate you can download it again from the Texas Instruments Web site at education ti com and then install the App again on your calculator An error occurred during the transfer The current OS in the receiving...

Page 719: ...transmit them to Texas Instruments so a group certificate can be issued A group certificate allows distribution of purchased software to multiple TI 89 Titanium TI 89 Voyage 200 or TI 92 Plus units The software can be loaded deleted from and reloaded to the devices as often as needed for as long as the software remains listed in the group certificate You may add new ID numbers and or new commercia...

Page 720: ...y the Home screen Press 2 Sending unit a Press 2 to display the VAR LINK screen b Press Link and select 6 Send ID List The sending unit adds a copy of its unique ID number to the collection unit s ID list The sending unit always retains its own ID number which cannot be deleted from the device 3 Additional units Repeat steps 1 and 2 until all the IDs are collected onto one device Depending on avai...

Page 721: ...remains on the collection device after it is uploaded to the computer You can then use the collection device to upload the list to other computers To clear the ID list from the collection unit 1 Press 2 to display the VAR LINK screen Compatibility among the TI 89 Titanium Voyage 200 TI 89 and TI 92 Plus In general TI 89 Titanium TI 89 Voyage 200 and TI 92 Plus data and programs are compatible with...

Page 722: ...s more memory and thus more room for applications Apps All data is compatible among the TI 89 Titanium TI 89 Voyage 200 and TI 92 Plus but some programs written for one may not run or may not run the same on the other because of differences in the device s screen sizes and keyboards and the USB port on the TI 89 Titanium Other incompatibilites can occur because of different version the operating s...

Page 723: ...yage 200 TI 92 Plus TI 89 Titanium OS Apps Variables Apps Variables Variables Variables TI 89 Apps Variables OS Apps Variables Variables Variables Voyage 200 Variables Variables OS Apps Variables Apps Variables TI 92 Plus Variables Variables Apps Variables OS Apps Variables ...

Page 724: ...hout tilting the pole Maximum Length of Pole in Hallway The maximum length of a pole c is the shortest line segment touching the interior corner and opposite sides of the two hallways as shown in the diagram below Use proportional sides and the Pythagorean theorem to find the length c with respect to w Then find the zeros of the first derivative of c w The minimum value of c w is the maximum lengt...

Page 725: ...te When you want to define a function use multiple character names as you build the definition 2 Define the expression for side b in terms of w and store it in b w 3 Define the expression for side c in terms of w and store it in c w Enter Define c w a w 2 b w 2 10 5 w a b c a w 5 b 10a w ...

Page 726: ...f c w to find the minimum value of c w Note The maximum length of the pole is the minimum value of c w 5 Compute the exact maximum length of the pole Enter c 2 6 Compute the approximate maximum length of the pole Result Approximately 20 8097 feet Note Use the auto paste feature to copy the result from step 4 to the entry line inside the parentheses of c and press 8 b b 2 4ac 2a ...

Page 727: ...ompleting the square of the generalized quadratic equation 1 Clear all one character variables in the current folder 2 ˆ Choose 1 Clear a z and press to confirm 2 On the Home screen enter the generalized quadratic equation ax2 bx c 0 3 Subtract c from both sides of the equation 2 j C Note This example uses the result of the last answer to perform computations on the TI 89 Titanium This feature red...

Page 728: ...ps 4 through 9 5 Use the expand function to expand the result of the last answer 6 Complete the square by adding b a 2 2 to both sides of the equation 7 Factor the result using the factor function 8 Multiply both sides of the equation by 4a2 9 Take the square root of both sides of the equation with the constraint that a 0 and b 0 and x 0 ...

Page 729: ...or x by subtracting b from both sides and then dividing by 2a Note This is only one of the two general quadratic solutions due to the constraint in step 9 1 On the Home screen use RandSeed to set the random number generator seed to the factory default and then use randMat to create a random 3x3 matrix and store it in a 2 Replace the 2 3 element of the matrix with the variable x and then use the au...

Page 730: ...rix b The result will have the identity matrix in the first three columns and a L1 in the last three columns Note Use the cursor in the history area to scroll the result 4 Solve for the value of x that will cause the inverse of the matrix to be invalid Enter solve getDenom 2 1 4 0 x Result x L70 17 Note Use the cursor in the history area to scroll the result ...

Page 731: ... cos x and 2 x sin x 2 In the Window Editor set xmin 0 and xmax 3p 3 Press and select A ZoomFit 4 Find the intersection point of the two functions Note Press and select 5 Intersection Respond to the screen prompts to select the two curves and the lower and upper bounds for intersection A 5 Note the x and y coordinates Repeat steps 4 and 5 to find the other intersections ...

Page 732: ...his example can be found in Symbolic Manipulation and 3D Graphing 1 On the Home screen enter solve sin x cos x x The solution for x is where n1 is any integer 2 Using the ceiling and floor functions find the ceiling and floor values for the intersection points as shown Note Move the cursor into the history area to highlight the last answer Press to copy the result of the general solution 3 Enter t...

Page 733: ...m surface area 1 On the Home screen define the function sa x y v for the surface area of a parallelepiped Enter define sa x y v 2 x y 2v x 2v y 2 Select the 3D Graph mode Then enter the function for z1 x y as shown in this example with volume v 300 3 Set the Window variables to eye 60 90 0 x 0 15 15 y 0 15 15 z 260 300 ncontour 5 4 Graph the function and use Trace to go to the point close to the m...

Page 734: ...ext Editor This activity shows you how to use the Text Editor to run a tutorial script 1 Solve for x and y in terms of v Enter solve d sa x y v x 0 and d sa x y v y 0 x y 2 Find the minimum surface area when the value of v equals 300 Enter 300 v Enter sa v 1 3 v 1 3 v Note Press to obtain the exact result in symbolic form Press 8 to obtain the approximate result in decimal form ...

Page 735: ...mmand toolbar menu 2 Type the following lines into the Text Editor 1 Open the Text Editor and create a new variable named demo1 C C C C C C Compute the maximum value of f on the closed interval a b assume that f is differentiable on a b define f x x 3N2x 2 xN7 1 a 3 22 b d f x x df x zeros df x x f ans 1 f a b The largest number from the previous two commands is the maximum value of the function T...

Page 736: ...and Symbolic Manipulation 3 Press and select 1 Script view to show the Text Editor and the Home screen on a split screen Move the cursor to the first line in the Text Editor 4 Press repeatedly to execute each line in the script one at a time Note Press and select 2 Clear split to go back to a full sized Text Editor screen 5 To see the results of the script on a full sized screen go to the Home scr...

Page 737: ... entries are displayed in reverse type in the example screens 2 Use the proper fraction function propFrac to split the function into a quotient and remainder 3 Copy the last answer to the entry line or Enter 16 xN2 x 2N8 xN17 Note Move the cursor into the history area to highlight the last answer Press to copy it to the entry line 4 Edit the last answer in the entry line Store the remainder to y1 ...

Page 738: ...hick graphing style for y2 x 6 Add the original function f x to y3 x and select the square graphing style 7 In the Window Editor set the window variables to x L10 15 10 y L100 100 10 8 Draw the graph Note Be sure the Graph mode is set to Function ...

Page 739: ...ression is basically a quadratic function as x gets very large in both the positive and negative directions Studying Statistics Filtering Data by Categories This activity provides a statistical study of the weights of high school students using categories to filter the data The lower graph is y3 x f x graphed separately using the line style ...

Page 740: ... vs Description Category C2 Academic Year and Sex 1 2 3 4 5 6 7 8 Freshman boys Freshman girls Sophomore boys Sophomore girls Junior boys Junior girls Senior boys Senior girls Table 2 C1 weight of each student in pounds vs C2 category C1 C2 C1 C2 C1 C2 C1 C2 110 125 105 120 140 85 80 90 80 95 1 1 1 1 1 2 2 2 2 2 115 135 110 130 150 90 95 85 100 95 3 3 3 3 3 4 4 4 4 4 130 145 140 145 165 100 105 11...

Page 741: ...Matrix Editor and create a new Data variable named students 2 Enter the data and categories from Table 2 into columns c1 and c2 respectively 3 Open the Plot Setup toolbar menu Note Set up several box plots to compare different subsets of the entire data set 4 Define the plot and filter parameters for Plot 1 as shown in this screen ...

Page 742: ...y the Include Categories item for Plot 2 through Plot 5 to the following Plot 2 1 2 freshman boys girls Plot 3 7 8 senior boys girls Plot 4 1 3 5 7 all boys Plot 5 2 4 6 8 all girls 8 In the Y Editor deselect any functions that may be selected from a previous activity Note Only Plot 1 through Plot 5 should be selected ...

Page 743: ... Experiment Workbook You can use your computer keyboard to type lengthy text and then use TI Connect software to send it to the calculator More CBL 2 programs are available from the TI Web site at educaton ti com 9 Display the plots by pressing and selecting 9 Zoomdata 10 Use the Trace tool to compare the median student weights for different subsets Ê median all students Ë all students Ì all fresh...

Page 744: ...TI 89 Titanium Program IO input output screen L10 xmin 99 xmax 10 xscl Set up the Window variables L20 ymin 100 ymax 10 yscl 0 data Create and or clear a list named data 0 time Create and or clear a list named time Send 1 0 Send a command to clear the CBL 2 unit Send 1 2 1 Set up Chan 2 of the CBL 2 to AutoID to record temp Disp Press ENTER to start Prompt the user to press Disp graphingTemperatur...

Page 745: ... the CBL 2 collect data in real time For i 1 99 Repeat next two instructions for 99 temperature readings Get data i Get a temperature from the CBL 2 and store it in a list PtOn i data i Plot the temperature data on a graph EndFor seq i i 1 99 1 time Create a list to represent time or data sample number NewPlot 1 1 time data 4 Plot time and data using NewPlot and the Trace tool DispG Display the gr...

Page 746: ...nd Table Perform the following steps to study the flight of a hit baseball that has an initial velocity of 95 feet per second and an initial angle of 32 degrees 1 Set the modes for Page 1 as shown in this screen 2 Set the modes for Page 2 as shown in this screen 3 In the Y Editor on the left side enter the equation for the distance of the ball at time t for xt1 t xt1 t 95 t cos 32 Note Press 2 to ...

Page 747: ...sin 32 5 Set the Window variables to t values 0 4 1 x values 0 300 50 y values 0 100 10 6 Switch to the right side and display the graph Note Press 2 a 7 Display the TABLE SETUP dialog box and change tblStart to 0 and tbl to 0 1 Note Press 8 8 Display the table in the left side and press D to highlight t 2 Note Press 8 ...

Page 748: ...ots Perform the following steps to expand the cubic polynomial xN1 xNi x i find the absolute value of the function graph the modulus surface and use the Trace tool to explore the modulus surface 9 Switch to the right side Press and trace the graph to show the values of xc and yc when tc 2 Note As you move the trace cursor from tc 0 0 to tc 3 1 you will see the position of the ball at time tc 1 On ...

Page 749: ...find the absolute value of f x yi This calculation may take about 2 minutes Note The absolute value of a function forces any roots to visually just touch rather than cross the x axis Likewise the absolute value of a function of two variables will force any roots to visually just touch the xy plane 4 Copy and paste the last answer to the entry line and store it in the function z1 x y Note The graph...

Page 750: ... In the Y Editor press 8 Í and set the Graph Format variables to Axes ON Labels ON Style HIDDEN SURFACE Note Calculating and drawing the graph takes about three minutes 7 Graph the modulus surface The 3D graph is used to visually display a picture of the roots where the surface touches the xy plane 8 Use the Trace tool to explore the function values at x 1 and y 0 ...

Page 751: ... three points where the graph of the modulus surface touches the xy plane Solving a Standard Annuity Problem This activity can be used to find the interest rate starting principal number of compounding periods and future value of an annuity 9 Use the Trace tool to explore the function values at x 0 and y 1 10 Use the Trace tool to explore the function values at x 0 and y L1 ...

Page 752: ...er of compounding periods n is 6 and the future value s is 2 000 1 On the Home screen enter the equation to solve for p 2 Enter the equation to solve for n 3 Enter the equation to solve for i using the with operator solve s p 1 i n i s 2000 and p 1000 and n 6 Result The interest rate is 12 246 Note To enter the with operator Í Press 8 to obtain a floating point result ...

Page 753: ...an item Detailed information about the steps used in this example can be found in Programming Time Value of Money Function In the Program Editor define the following Time Value of Money tvm function where temp1 number of payments temp2 annual interest rate temp3 present value temp4 monthly payment temp5 future value and temp6 begin or end of payment Enter the equation to solve for s solve s p 1 i ...

Page 754: ...temp4 temp5 temp6 Func Local tempi tempfunc tempstr1 Ltemp3 1 temp2 1200 temp6 temp4 1N 1 temp2 1200 Ltemp1 temp2 1200 Ntemp5 1 temp2 1200 Ltemp1 tempfunc For tempi 1 5 1 temp exact string tempi tempstr1 If when tempstr1 0 false false true Then If tempi 2 Return approx nsolve tempfunc 0 tempstr1 tempstr1 0 and tempstr1 100 Return approx nsolve tempfunc 0 tempstr1 EndIf EndFor Return parameter erro...

Page 755: ...ld make a 300 payment each month Finding Rational Real and Complex Factors This activity shows how to find rational real or complex factors of expressions Detailed information about the steps used in this example can be found in Symbolic Manipulation On the Home screen enter the tvm values to find pmt Result The monthly payment is 251 53 On the Home screen enter the tvm values to find n Result The...

Page 756: ...bout the steps used in this example can be found in Programming Sampling without Replacement Function In the Program Editor define drawball as a function that can be called with two parameters The first parameter is a list where each element is the number of balls of a 1 factor x 3N5x displays a rational result 2 factor x 3 5x displays a rational result 3 factor x 3N5x x displays a real result 4 c...

Page 757: ...ordim numballs i pick urncum j If drawnum sum urnlist Return too few balls dim urnlist colordim urnlist templist newlist colordim drawlist For i 1 drawnum 1 sum templist numballs rand numballs pick continued in next column For j 1 colordim 1 cumSum templist urncum If pick urncum j Then drawlist j 1 drawlist j templist j N1 templist j Exit EndIf EndFor EndFor Return drawlist EndFunc 1 Enter a rando...

Page 758: ...force of the current carries the boat along so it actually travels at a 60 angle with the shore How fast is the current and how fast does the boat actually travel 1 Set the modes for Page 1 as shown in this screen Show angles in degrees instead of radians and display all digits with a floating decimal point Press 3 D D D On the Angle option select 2 DEGREE On the Display Digits option select E FLO...

Page 759: ... as i c and r Use the value a for the unknown speed of the current Use the value b for the speed of the boat Enter 20 80 i a 0 c b 60 r Vectors are commonly written in either polar or rectangular form so it is useful to convert polar vectors into rectangular form 3 Define function p2r Enter Define p2r x x 1 1 cos x 1 2 x 1 1 sin x 1 2 ...

Page 760: ...ors are equal the x coordinate of i c must equal the x coordinate of the resultant vector r Likewise the y coordinate of i c must equal the y coordinate of resultant vector r 5 Set up two equations involving vectors i c and r Equation 1 sets the x coordinates equal to each other Equation 2 sets the y coordinates equal Store these equations into eq1 and eq2 respectively Enter i 1 1 c 1 1 r 1 1 eq1 ...

Page 761: ... speed of the boat solve eq2 b 7 Substitute the known value of b into eq1 and solve eq1 for a to determine a the speed of the eastward traveling current solve eq1 a b The boat travels at a speed of 22 7 knots and the water current is approximately 7 9 knots ...

Page 762: ...tion that is included in the operating system OS See modules relating to calculator software applications Apps for functions and instructions specific to those Apps Circle CATALOG Circle x y r drawMode Draws a circle with its center at window coordinates x y and with a radius of r x y and r must be real values If drawMode 1 draws the circle default If drawMode 0 turns off the circle If drawMode 1 ...

Page 763: ...30 PxlChg 830 PxlCrcl 830 PxlHorz 830 PxlLine 830 PxlOff 831 PxlOn 831 pxlTest 831 PxlText 831 PxlVert 831 RclGDB 835 RclPic 835 RplcPic 839 Shade 846 StoGDB 855 StoPic 856 Style 856 Trace 863 XorPic 867 ZoomBox 869 ZoomData 870 ZoomDec 870 ZoomFit 871 ZoomIn 871 ZoomInt 871 ZoomOut 872 ZoomPrev 872 ZoomRcl 872 ZoomSqr 872 ZoomStd 873 ZoomSto 873 ZoomTrig 873 add 873 ì subtract 874 ù multiply 874 ...

Page 764: ...7 nCr 818 nPr 821 P4Rx 824 P4Ry 824 r radian 882 R4Pq 833 R4Pr 834 real 835 remain 836 rotate 837 round 838 sec 840 secê 840 sech 840 sechê 840 shift 847 sign 848 sin 849 sinê 849 sinh 850 sinhê 850 tan 859 tanê 859 tanh 859 tanhê 860 tmpCnv 862 tmpCnv 863 xê 884 add 873 ì subtract 874 ù multiply 874 à divide 875 ë negate 877 dot add 876 dot subt 876 dot mult 877 dot divide 877 dot power 877 power...

Page 765: ...799 Get 799 GetCalc 799 getConfg 800 getDate 800 getDtFmt 801 getDtStr 801 getFold 801 getKey 801 getMode 802 getTime 802 getTmFmt 802 getTmStr 802 getTmZn 803 getType 803 getUnits 803 Goto 804 If 805 Input 806 InputStr 807 isClkOn 808 Item 808 Lbl 808 left 809 Local 812 Lock 812 Loop 814 MoveVar 817 NewFold 819 NewProb 820 not 821 or 823 Output 823 part 824 PassErr 826 Pause 826 PopUp 827 Prgm 82...

Page 766: ...wData 818 NewPlot 820 nPr 821 OneVar 822 PlotsOff 827 PlotsOn 827 PowerReg 828 QuadReg 832 QuartReg 833 rand 834 randNorm 834 RandSeed 834 ShowStat 848 SinReg 851 SortA 854 SortD 854 stdDev 855 TwoVar 864 variance 865 append 880 indirection 881 char 769 dim 787 expr 794 format 798 inString 807 left 809 mid 816 ord 823 right 837 rotate 837 shift 847 string 856 Statistics Strings ...

Page 767: ...e represents the bit results and is displayed according to the Base mode You can enter the integers in any number base For a binary or hexadecimal entry you must use the 0b or 0h prefix respectively Without a prefix integers are treated as decimal base 10 If you enter a decimal integer that is too large for a signed 32 bit binary form a symmetric modulo operation is used to bring the value into th...

Page 768: ...ble PIC1 y2 x sin x 2ˆ Style 3 Square H ˆ Style 3 Square y1 no checkmark F4 to deselect Zoom 7 ZoomTrig H AndPic PIC1 Done angle MATH Complex menu angle expression1 expression Returns the angle of expression1 interpreting expression1 as a complex number Note All undefined variables are treated as real variables In Degree angle mode angle 0 2i 90 In Radian angle mode angle 1 i p 4 angle z angle x i...

Page 769: ... CATALOG Archive var1 var2 var3 Moves the specified variables from RAM to the user data archive memory You can access an archived variable the same as you would a variable in RAM However you cannot delete rename or store to an archived variable because it is locked automatically To unarchive variables use Unarchiv 10 arctest 10 Archive arctest Done 5ùarctest 50 15 arctest N Unarchiv arctest Done 1...

Page 770: ... is the step value If h is omitted it defaults to 0 001 Note that the similar function nDeriv uses the central difference quotient avgRC f x x h f x h f x h avgRC sin x x h x 2 sin h 2 sin 2 h avgRC x 2ìx 2 x 2 ø x 4995 avgRC x 2ìx 2 x 1 2 ø x 45 avgRC x 2ìx 2 x 3 2ø x 1 4Bin MATH Base menu integer1 4Bin integer Converts integer1 to a binary number Binary or hexadecimal numbers always have a 0b or...

Page 771: ...s through its range of values Then x increments to its next value and y again increments through its range This pattern continues until x has incremented through its range Note The following sample data is from a 3D graph ceiling MATH Number menu ceiling expression1 integer Returns the nearest integer that is the argument The argument can be a real or a complex number Note See also floor ceiling 0...

Page 772: ... also factor cFactor x 5 4x 4 5x 3ì6xì3 x5 4øx4 5øx3 ì6øxì3 cFactor ans 1 x x ì 965 ø x 612 ø x 2 13 ø x 1 11 ì 1 07øi ø x 1 11 1 07øi char MATH String menu char integer character Returns a character string containing the character numbered integer from the TI 89 Titanium Voyage 200 character set See Appendix B for a complete listing of character codes The valid range for integer is 0 255 char 38 ...

Page 773: ...r or PassErr If the error is to be processed or ignored use ClrErr If what to do with the error is not known use PassErr to send it to the next error handler If there are no more pending Try EndTry error handlers the error dialog box will be displayed as normal Note See also PassErr and Try Program listing clearerr Prgm PlotsOff FnOff ZoomStd For i 0 238 xù i xmin xcord Try PtOn xcord ln xcord Els...

Page 774: ...the Table screen in Ask mode you can clear the values by pressing ƒ and selecting 8 Clear Table colDim MATH Matrix Dimensions menu colDim matrix expression Returns the number of columns contained in matrix Note See also rowDim colDim 0 1 2 3 4 5 3 colNorm MATH Matrix Norms menu colNorm matrix expression Returns the maximum of the sums of the absolute values of the elements in the columns in matrix...

Page 775: ...st memory comDenom exprn abc comden exprn Done comden y 2 y x 1 2 y 2 y Even when there is no denominator the comden function is often a fast way to achieve partial factorization if factor is too slow or if it exhausts memory Hint Enter this comden function definition and routinely try it as an alternative to comDenom and factor comden 1234x 2ù y 3ì y 2468x ù y 2ì 1 1234ø xø xø y 2 ø yñ ì 1 conj M...

Page 776: ...culated by the algorithm 1 Compute the eigenvalues li and eigenvectors Vi of A squareMatrix1 must be diagonalizable Also it cannot have symbolic variables that have not been assigned a value 2 Form the matrices B l1 0 0 0 l2 0 0 0 0 0 0 ln and X V1 V2 Vn 3 Then A X B Xê and f A X f B Xê For example cos A X cos B Xê where cos B cos cos cos λ λ λ 1 2 0 0 0 0 0 0 0 0 0 K K K K n All computations are ...

Page 777: ...g point numbers In Radian angle mode cosh 1 5 3 4 2 1 6 ë 2 1 421 255 253 909 216 905 327 635 255 301 202 958 226 297 216 623 167 628 coshê MATH Hyperbolic menu coshê expression1 expression coshê list1 list coshê expression1 returns the inverse hyperbolic cosine of the argument as an expression coshê list1 returns a list of the inverse hyperbolic cosines of each element of list1 coshê 1 0 coshê 1 ...

Page 778: ...g the inverse hyperbolic cotangents of each element of list1 cothL1 3 5 293 cothL1 L2 2 1 6 Lln 3 2 518 ln 7 5 2 crossP MATH Matrix Vector ops menu crossP list1 list2 list Returns the cross product of list1 and list2 as a list list1 and list2 must have equal dimension and the dimension must be either 2 or 3 crossP a1 b1 a2 b2 0 0 a1ø b2ì a2ø b1 crossP 0 1 2 2 ë 5 1 ë 5 0 ë 2 5 ë 5 ë 2 25 crossP ve...

Page 779: ...al is to produce candidates for all real and non real solutions Even if equation is real cSolve allows non real results in real mode Although the TI 89 Titanium Voyage 200 processes all undefined variables that do not end with an underscore _ as if they were real cSolve can solve polynomial equations for complex solutions cSolve x 3 ë 1 x solve x 3 ë 1 x cSolve temporarily sets the domain to compl...

Page 780: ... include both real and non real solutions as in the example to the right cSolve u_ù v_ì u_ v_ and v_ 2 ë u_ u_ v_ u_ 1 2 3 2 øi and v_ 1 2 ì 3 2 øi or u_ 1 2 ì 3 2 øi and v_ 1 2 3 2 øi or u_ 0 and v_ 0 Simultaneous polynomial equations can have extra variables that have no values but represent given numeric values that could be substituted later cSolve u_ù v_ì u_ c_ù v_ and v_ 2 ë u_ u_ v_ u_ ë 1ì...

Page 781: ...4 891 øi and z_ 1 588 1 540 øi CubicReg MATH Statistics Regressions menu CubicReg list1 list2 list3 list4 list5 Calculates the cubic polynomial regression and updates all the statistics variables All the lists must have equal dimensions except for list5 list1 represents xlist list2 represents ylist list3 represents frequency list4 represents category codes list5 represents category include list No...

Page 782: ...ivated when you press 2 It is very similar to the ToolBar instruction except that Title and Item statements cannot have labels block can be either a single statement or a series of statements separated with the character Note 2 acts as a toggle The first instance invokes the menu and the second instance removes the menu The menu is removed also when you change applications Program listing Test Prg...

Page 783: ...e also cSolve solve and zeros Display Digits mode in Fix 3 cZeros x 5 4x 4 5x 3ì 6xì 3 x ë 2 125 ë 612 965 ë 1 114 ì 1 073ø i ë 1 114 1 073ø i Note If expression is non polynomial with functions such as abs angle conj real or imag you should place an underscore _ q H 2 q at the end of var By default a variable is treated as a real value If you use var_ the variable is treated as complex You should...

Page 784: ...e For polynomial systems computation time or memory exhaustion may depend strongly on the order in which you list unknowns If your initial choice exhausts memory or your patience try rearranging the variables in the expressions and or varOrGuess list cZeros u_ù v_ì u_ì v_ v_ 2 u_ u_ v_ w_ 1 2 ì 3 2 øi 1 2 3 2 øi 1 1 2 3 2 øi 1 2 ì 3 2 øi 1 0 0 1 If you do not include any guesses and if any express...

Page 785: ...3ì x 7 x 2 18ø x d f x ù g x x d dx f x ø g x d dx g x ø f x d sin f x x cos f x d dx f x d x 3 x x 5 75 d d x 2ù y 3 x y 6ø yñ ø x d x 2 x ë 1 xò 3 d x 2 x 3 x 4 x 2ø x 3ø xñ 4ø xò dayOfWk CATALOG dayOfWk year month day integer Returns an integer from 1 to 7 with each integer representing a day of the week Use dayOfWk to determine on which day of the week a particular date would occur Note May no...

Page 786: ...ine a 3 Define g x y 2xì 3y Done g 1 2 ë 4 1 a 2 b g a b ë 4 Define h x when x 2 2x 3 ë 2x 3 Done h ë 3 ë 9 h 4 ë 5 Define eigenvl a cZeros det identity dim a 1 xù a x Done eigenvl ë 1 2 4 3 2ø 3 1 11 ë 2ø 3 1 11 Define funcName arg1Name arg2Name Func block EndFunc Is identical to the previous form of Define except that in this form the user defined function funcName can execute a block of multipl...

Page 787: ...ewFold games Done creates the folder games DelFold games Done deletes the folder games DelVar CATALOG DelVar var1 var2 var3 Deletes the specified variables from memory 2 a 2 a 2 2 16 DelVar a Done a 2 2 a 2 ñ deSolve MATH Calculus menu deSolve 1stOr2ndOrderOde independentVar dependentVar a general solution Returns an equation that explicitly or implicitly specifies a general solution to the 1st or...

Page 788: ...itialCondition is an equation of the form dependentVar initialIndependentValue initialDependentValue The initialIndependentValue and initialDependentValue can be variables such as x0 and y0 that have no stored values Implicit differentiation can help verify implicit solutions sin y yù e x cos y y ode sin y ex øy cos y øy deSolve ode and y 0 0 x y soln ë 2øsin y yñ 2 ë ex ì1 øeëx øsin y soln x 0 an...

Page 789: ... 3 ë 2 4 1 ë 6 ë 2 7 ë 98ø xò ì 55ø xñ 12ø x ì 1 1E20 1 0 1 mat1 1 E20 1 0 1 det mat1 0 det mat1 1 1 E20 diag MATH Matrix menu diag list matrix diag rowMatrix matrix diag columnMatrix matrix Returns a matrix with the values in the argument list or matrix in its main diagonal diag 2 4 6 2 0 0 0 4 0 0 0 6 diag squareMatrix rowMatrix Returns a row matrix containing the elements from the main diagonal...

Page 790: ... O screen An expression can include conversion operations such as 4DD and 4Rect You can also use the 4 operator to perform unit and number base conversions If Pretty Print ON expressions are displayed in pretty print From the Program I O screen you can press to display the Home screen or a program can use DispHome Disp Hello Hello Disp cos 2 3 ë 666 1 2 3 4 L1 Disp L1 1 2 3 4 Disp 180_min 4 _hr 3 ...

Page 791: ...371 4DMS 45ó 22 15 6 45 371 60 4DMS 45ó 22 15 6 60ó dotP MATH Matrix Vector ops menu dotP list1 list2 expression Returns the dot product of two lists dotP a b c d e f aø d bø e cø f dotP 1 2 5 6 17 dotP vector1 vector2 expression Returns the dot product of two vectors Both must be row vectors or both must be column vectors dotP a b c d e f aø d bø e cø f dotP 1 2 3 4 5 6 32 DrawFunc CATALOG DrawFu...

Page 792: ... the window settings If the current graphing mode is not polar these three arguments are required Note Regraphing erases all drawn items In function graphing mode and ZoomStd window DrawPol 5ù cos 3ù q 0 3 5 1 DrawSlp CATALOG DrawSlp x1 y1 slope Displays the graph and draws a line using the formula yì y1 slopeø xì x1 Note Regraphing erases all drawn items In function graphing mode and ZoomStd wind...

Page 793: ...saEexponent Enters a number in scientific notation The number is interpreted as mantissa 10exponent Hint If you want to enter a power of 10 without causing a decimal value result use 10 integer 2 3í 4 23000 2 3í 9 4 1í 15 4 1í 15 3ù 10 4 30000 e skey H 2 s key e expression1 expression Returns e raised to the expression1 power Note On the TI 89 Titanium pressing s to display e is different from pre...

Page 794: ...x menu eigVl squareMatrix list Returns a list of the eigenvalues of a real or complex squareMatrix squareMatrix is first balanced with similarity transformations until the row and column norms are as close to the same value as possible The squareMatrix is then reduced to upper Hessenberg form and the eigenvalues are computed from the upper Hessenberg matrix In Rectangular complex format mode L1 2 ...

Page 795: ...cannot be an expression Note If the last entry is still highlighted on the Home screen pressing is equivalent to executing entry 1 On the Home screen 1 1 x 1 x 1 1 1 entry 1 2ì 1 x 1 1 2ø 2ø x 1 3 2 5 3ì 1 3ø 3ø x 2 entry 4 1 x 1 exact MATH Number menu exact expression1 tol expression exact list1 tol list exact matrix1 tol matrix Uses Exact mode arithmetic regardless of the Exact Approx mode setti...

Page 796: ...CATALOG exp4list expression var list Examines expression for equations that are separated by the word or and returns a list containing the right hand sides of the equations of the form var expression This gives you an easy way to extract some solution values embedded in the results of the solve cSolve fMin and fMax functions Note exp4list is not necessary with the zeros and cZeros functions becaus...

Page 797: ...enom for an expanded numerator over an expanded denominator expand x 3 x 2ì 2 x 2ì 2 2ø x xñ ì 2 x 1 expand ans 1 x 1 xì 2 1 x 2 x 1 expand expression1 var also distributes logarithms and fractional powers regardless of var For increased distribution of logarithms and fractional powers inequality constraints might be necessary to guarantee that some factors are nonnegative expand expression1 var a...

Page 798: ...enominator expression1 is factored as much as possible toward linear rational factors without introducing new non real subexpressions This alternative is appropriate if you want factorization with respect to more than one variable factor a 3ù x 2ì aù x 2ì a 3 a aø a ì1 ø a 1 ø x ì1 ø x 1 factor x 2 1 xñ 1 factor x 2ì 4 x ì 2 ø x 2 factor x 2ì 3 xñ ì 3 factor x 2ì a xñ ì a factor expression1 var re...

Page 799: ... want to determine if a number is prime use isPrime instead It is much faster particularly if rationalNumber is not prime and if the second largest factor has more than five digits factor 152417172689 123457ø1234577 isPrime 152417172689 false Fill MATH Matrix menu Fill expression matrixVar matrix Replaces each element in variable matrixVar with expression matrixVar must already exist 1 2 3 4 amatr...

Page 800: ... often faster particularly if you use the operator to constrain the search to a relatively small interval that contains exactly one local minimum Note See also fMax and min fMin 1ì xì a 2ì xì b 2 x x ˆ or x ë ˆ fMin 5x 3ì xì 2 x x 1 x 1 fMin aù x 2 x x ˆ or x ë ˆ or x 0 or a 0 fMin aù x 2 x a 0 and x 1 x 1 fMin aù x 2 x a 0 x 0 FnOff CATALOG FnOff Deselects all Y functions for the current graphing...

Page 801: ...n Scientific format n is the number of digits to display after the decimal point E n Engineering format n is the number of digits after the first significant digit The exponent is adjusted to a multiple of three and the decimal point is moved to the right by zero one or two digits format 1 234567 f3 1 235 format 1 234567 s2 1 23í 0 format 1 234567 e3 1 235í 0 format 1 234567 g3 1 235 format 1234 5...

Page 802: ...al floating point numbers is 1 0 gcd 18 33 3 gcd list1 list2 list Returns the greatest common divisors of the corresponding elements in list1 and list2 gcd 12 14 16 9 7 5 3 7 1 gcd matrix1 matrix2 matrix Returns the greatest common divisors of the corresponding elements in matrix1 and matrix2 gcd 2 4 6 8 4 8 12 16 2 4 6 8 Get CATALOG Get var Retrieves a CBL 2é CBL Calculator Based Laboratoryé or C...

Page 803: ...99 Product ID 03 1 4 68 ID 01012 34567 ABCD Cert Rev 0 Screen Width 160 Screen Height 100 Window Width 160 Window Height 67 RAM Size 262132 Free RAM 197178 Archive Size 655360 Free Archive 655340 H getConfg Product Name Advanced Mathematics Software Version 2 00 09 25 1999 Product ID 01 1 4 80 ID 01012 34567 ABCD Cert Rev 0 Screen Width 240 Screen Height 120 Window Width 240 Window Height 91 RAM S...

Page 804: ...day of September 2002 when the date format is set to DD MM YY If you enter the optional integer that corresponds to a date format the string returns the current date in the specified format Optional integer values 1 MM DD YY 2 DD MM YY 3 MM DD YY 4 DD MM YY 5 YY MM DD 6 MM DD YY 7 DD MM YY 8 YY MM DD getFold CATALOG getFold nameString Returns the name of the current folder as a string getFold main...

Page 805: ...lit 1 App Home Split 2 App Graph Number of Graphs 1 Graph 2 FUNCTION Split Screen Ratio 1 1 Exact Approx AUTO Base DEC Note Your screen may display different mode settings getNum MATH Algebra Extract menu getNum expression1 expression Transforms expression1 into one having a reduced common denominator and then returns its numerator getNum x 2 yì 3 x 2 getNum 2 7 2 getNum 1 x 1 y x y getTime CATALO...

Page 806: ... 2 3 temp 1 2 3 getType temp LIST 2 3i temp 2 3i getType temp EXPR DelVar temp Done getType temp NONE Data Type Variable Contents ASM Assembly language program DATA Data type EXPR Expression includes complex arbitrary undefined ˆ ë ˆ TRUE FALSE pi e FUNC Function GDB Graph data base LIST List MAT Matrix NONE Variable does not exist NUM Real number OTHER Miscellaneous data type for future use by so...

Page 807: ... an optional var argument Graph uses the independent variable of the current graphing mode Note Not all optional arguments are valid in all modes because you can never have all four arguments at the same time In function graphing mode and ZoomStd window Graph 1 25aù cos a a In parametric graphing mode and ZoomStd window Graph time 2cos time time time Some valid variations of this instruction are F...

Page 808: ...evaluates to true executes the single statement statement or the block of statements block before continuing execution If Boolean expression evaluates to false continues execution without executing the statement or block of statements block can be either a single statement or a sequence of statements separated with the character Program segment If x 0 Disp x is negative or If x 0 Then Disp x is ne...

Page 809: ...2i 2 imag z 0 imag x iy y imag list1 list Returns a list of the imaginary parts of the elements imag ë 3 4ë i i 0 ë 1 1 imag matrix1 matrix Returns a matrix of the imaginary parts of the elements imag a b ic id 0 0 c d Indirection See page 881 Input CATALOG Input Pauses the program displays the current Graph screen and lets you update variables xc and yc also rc and qc for polar coordinate mode by...

Page 810: ...ring Hello there the 7 ABCEFG s1 If inString s1 D 0 Disp D not found D not found int CATALOG int expression integer int list1 list int matrix1 matrix Returns the greatest integer that is less than or equal to the argument This function is identical to floor The argument can be a real or a complex number For a list or matrix returns the greatest integer of each of the elements int ë 2 5 ë 3 int 1 2...

Page 811: ...ring label Valid only within a Custom EndCustm or ToolBar EndTBar block Sets up a drop down menu element to let you paste text to the cursor position Custom or branch to a label ToolBar Note Branching to a label is not allowed within a Custom block See Custom example Lbl CATALOG Lbl labelName Defines a label with the name labelName in the program You can use a Goto labelName instruction to transfe...

Page 812: ...h h 0 cos x limit 1 1 n n n ˆ e Limits at positive ˆ and at negative ˆ are always converted to one sided limits from the finite side Depending on the circumstances limit returns itself or undef when it cannot determine a unique limit This does not necessarily mean that a unique limit does not exist undef means that the result is either an unknown number with finite or infinite magnitude or it is t...

Page 813: ...ff or off to on inverts pixels along the line Note Regraphing erases all drawn items See also PxlHorz In a ZoomStd window LineHorz 2 5 LineTan CATALOG LineTan expression1 expression2 Displays the Graph screen and draws a line tangent to expression1 at the point specified expression1 is an expression or the name of a function where x is assumed to be the independent variable and expression2 is the ...

Page 814: ...TH List menu list list1 list Returns a list containing the differences between consecutive elements in list1 Each element of list1 is subtracted from the next element of list1 The resulting list is always one element shorter than the original list1 list 20 30 45 70 10 15 25 list4mat MATH List menu list4mat list elementsPerRow matrix Returns a matrix filled row by row with the elements from list el...

Page 815: ...name and cannot be c1 c99 In function graphing mode 1 2 3 4 5 6 7 8 L1 1 2 3 1 2 2 3 3 3 4 4 L2 1 2 2 LnReg L1 L2 Done ShowStat Regeq x y1 x Done NewPlot 1 1 L1 L2 Done Local CATALOG Local var1 var2 var3 Declares the specified vars as local variables Those variables exist only during evaluation of a program or function and are deleted when the program or function finishes execution Note Local vari...

Page 816: ...647 øi 194 ì 315 øi 462 270øi ë 115 ì 904 øi 488 777 øi Logistic MATH Statistics Regressions menu Logistic list1 list2 iterations list3 list4 list5 Calculates the logistic regression and updates all the system statistics variables All the lists must have equal dimensions except for list5 list1 represents xlist list2 represents ylist list3 represents frequency list4 represents category codes list5 ...

Page 817: ...row swaps done during the calculation in pMatName lMatName ù uMatName pMatName ù matrix Optionally any matrix element is treated as zero if its absolute value is less than tol This tolerance is used only if the matrix has floating point entries and does not contain any symbolic variables that have not been assigned a value Otherwise tol is ignored If you use or set the mode to Exact Approx APPROXI...

Page 818: ...rix1 Note See also fMax and min max 1 ë 3 7 ë 4 0 3 1 0 7 mean MATH Statistics menu mean list freqlist expression Returns the mean of the elements in list Each freqlist element counts the number of consecutive occurrences of the corresponding element in list mean 2 0 1 ë 3 4 26 mean 1 2 3 3 2 1 5 3 mean matrix1 freqmatrix matrix Returns a row vector of the means of all the columns in matrix1 Each ...

Page 819: ...eater than the dimension of sourceString returns all characters from sourceString beginning with character number start count must be 0 If count 0 returns an empty string mid Hello there 2 ello there mid Hello there 7 3 the mid Hello there 1 5 Hello mid Hello there 1 0 mid sourceList start count list Returns count elements from sourceList beginning with element number start If count is omitted or ...

Page 820: ... lists or two matrices returns a list or matrix containing the modulo of each pair of corresponding elements Note See also remain mod 7 0 7 mod 7 3 1 mod ë 7 3 2 mod 7 ë 3 ë 2 mod ë 7 ë 3 ë 1 mod 12 ë 14 16 9 7 ë 5 3 0 ë 4 MoveVar CATALOG MoveVar var oldFolder newFolder Moves variable var from oldFolder to newFolder If newFolder does not exist MoveVar creates it 1 2 3 4 L1 1 2 3 4 MoveVar L1 Main ...

Page 821: ...st be the same size matrix nCr 6 5 4 3 2 2 2 2 15 10 6 3 nDeriv MATH Calculus menu nDeriv expression1 var h expression nDeriv expression1 var list list nDeriv list var h list nDeriv matrix var h matrix Returns the numerical derivative as an expression Uses the central difference quotient formula h is the step value If h is omitted it defaults to 0 001 When using list or matrix the operation gets m...

Page 822: ... is zero newList 4 0 0 0 0 newMat CATALOG also Math Matrix menu newMat numRows numColumns matrix Returns a matrix of zeros with the dimension numRows by numColumns newMat 2 3 0 0 0 0 0 0 NewPic CATALOG NewPic matrix picVar maxRow maxCol Creates a pic variable picVar based on matrix matrix must be an n 2 matrix in which each row represents a pixel Pixel coordinates start at 0 0 If picVar already ex...

Page 823: ...from a cleared state without resetting the memory Clears all single character variable names Clear a z in the current folder unless the variables are locked or archived Turns off all functions and stat plots FnOff and PlotsOff in the current graphing mode Perfoms ClrDraw ClrErr ClrGraph ClrHome ClrIO and ClrTable NewProb Done nInt MATH Calculus menu nInt expression1 var lower upper expression If t...

Page 824: ...dulo operation is used to bring the value into the appropriate range In Hex base mode not 0h7AC36 0hFFF853C9 In Bin base mode 0b100101 4 dec 37 not 0b100101 0b11111111111111111111111111011010 ans 1 4 dec ë 38 Note A binary entry can have up to 32 digits not counting the 0b prefix A hexadecimal entry can have up to 8 digits Note To type the 4 conversion operator press 2 p You can also select base c...

Page 825: ...where the residual is zero or two relatively close points where the residual has opposite signs and the magnitude of the residual is not excessive If it cannot achieve this using a modest number of sample points it returns the string no solution found If you use nSolve in a program you can use getType to check for a numeric result before using it in an algebraic expression Note See also cSolve cZe...

Page 826: ...ned 32 bit binary form a symmetric modulo operation is used to bring the value into the appropriate range Note See xor In Hex base mode 0h7AC36 or 0h3D5F 0h7BD7F In Bin base mode 0b100101 or 0b100 0b100101 Note A binary entry can have up to 32 digits not counting the 0b prefix A hexadecimal entry can have up to 8 digits ord MATH String menu ord string integer ord list1 list Returns the numeric cod...

Page 827: ...0 part CATALOG part expression1 nonNegativeInteger This advanced programming function lets you identify and extract all of the sub expressions in the simplified result of expression1 For example if expression1 simplifies to cos pù x 3 The cos function has one argument pù x 3 The sum of pù x 3 has two operands pù x and 3 The number 3 has no arguments or operands The product pù x has two operands p ...

Page 828: ... 3 0 cos part cos pù x 3 1 temp 3 pøx temp pøx 3 part temp 0 part temp 2 part temp 2 3 part temp 1 temp pøx part temp 0 ù part temp 2 part temp 1 p part temp 2 x Expressions such as x y z and xì yì z are represented internally as x y z and xì y ì z This affects the values returned for the first and second argument There are technical reasons why part x y z 1 returns y x instead of x y part x y z 2...

Page 829: ...to the next level If errornum is zero PassErr does not do anything The Else clause in the program should use ClrErr or PassErr If the error is to be processed or ignored use ClrErr If what to do with the error is not known use PassErr to send it to the next error handler See also ClrErr See ClrErr program listing example Pause CATALOG Pause expression Suspends program execution If you include expr...

Page 830: ... Radian angle mode returns reiq complexValue can have any complex form However an reiq entry causes an error in Degree angle mode Note You must use the parentheses for an roq polar entry In Radian angle mode 3 4i4Polar e i ø p 2 ì tanê 3 4 ø5 4op 3 4Polar e iøp 3 ø4 In Degree angle mode 3 4i4Polar 5o90ì tanê 3 4 polyEval MATH List menu polyEval list1 expression1 expression polyEval list1 list2 exp...

Page 831: ...ALOG Prgm EndPrgm Required instruction that identifies the beginning of a program Last line of program must be EndPrgm Program segment prgmname Prgm EndPrgm Product PI See Π page 881 product MATH List menu product list start end expression Returns the product of the elements contained in list Start and end are optional They specify a range of elements product 1 2 3 4 24 product 2 x y 2ø xø y produ...

Page 832: ...ts of the polynomial part are then made proper with respect to their most main variable first and so on For rational expressions propFrac is a faster but less extreme alternative to expand propFrac x 2 x 1 x 1 y 2 y 1 y 1 x propFrac ans 1 PtChg CATALOG PtChg x y PtChg xList yList Displays the Graph screen and reverses the screen pixel nearest to window coordinates x y Note PtChg through PtText sho...

Page 833: ...drawMode 1 inverts pixels along the circle Note Regraphing erases all drawn items See also Circle PxlCrcl 40 80 30 1 H PxlCrcl 50 125 40 1 PxlHorz CATALOG PxlHorz row drawMode Displays the Graph screen and draws a horizontal line at pixel position row If drawMode 1 draws the line default If drawMode 0 turns off the line If drawMode 1 turns a line that is on to off or off to on inverts pixels along...

Page 834: ...lse if the pixel is off Note Regraphing erases all drawn items PxlOn 25 50 H PxlTest 25 50 true PxlOff 25 50 H PxlTest 25 50 false PxlText CATALOG PxlText string row col Displays the Graph screen and places character string string on the screen starting at pixel coordinates row col string is positioned with the upper left corner of its first character at the coordinates Note Regraphing erases all ...

Page 835: ...o be calculated in floating point form 1 2 3 4 5 6 7 8 9 m1 1 2 3 4 5 6 7 8 9 QR m1 qm rm Done qm 123 904 408 492 301 ë 816 861 ë 301 408 rm 8 124 9 601 11 078 0 904 1 809 0 0 0 m n o p m1 m n o p The QR factorization is computed numerically using Householder transformations The symbolic solution is computed using Gram Schmidt The columns in qMatName are the orthonormal basis vectors that span the...

Page 836: ...y list4 represents category codes list5 represents category include list Note list1 through list4 must be a variable name or c1 c99 columns in the last data variable shown in the Data Matrix Editor list5 does not have to be a variable name and cannot be c1 c99 In function graphing mode ë 2 ë 1 0 1 2 3 4 5 6 L1 ë 2 ë 1 0 4 3 1 2 4 2 1 4 6 L2 4 3 1 QuartReg L1 L2 Done ShowStat Regeq x y1 x Done NewP...

Page 837: ... to integers RandSeed 1147 Done randMat 3 3 8 ë 3 6 ë 2 3 ë 6 0 4 ë 6 Note The values in this matrix will change each time you press randNorm MATH Probability menu randNorm mean sd expression Returns a decimal number from the specific normal distribution It could be any real number but will be heavily concentrated in the interval mean 3ù sd mean 3ù sd RandSeed 1147 Done randNorm 0 1 492 randNorm 3...

Page 838: ...l parts of all elements real a iù b 3 i a 3 0 real matrix1 matrix Returns the real parts of all elements real a iù b 3 c i a 3 c 0 4Rect MATH Matrix Vector ops menu vector 4Rect Displays vector in rectangular form x y z The vector must be of dimension 2 or 3 and can be a row or a column Note 4Rect is a display format instruction not a conversion function You can use it only at the end of an entry ...

Page 839: ... remain matrix1 matrix2 matrix Returns the remainder of the first argument with respect to the second argument as defined by the identities remain x 0 r x remain x y r xì yùiPart x y remain 7 0 7 remain 7 3 1 remain ë 7 3 ë 1 remain 7 ë 3 1 remain ë 7 ë 3 ë 1 remain 12 ë 14 16 9 7 ë 5 3 0 1 As a consequence note that remain ì x y r ì remain x y The result is either zero or it has the same sign as ...

Page 840: ...ide of an equation or inequality right x 3 3 rotate MATH Base menu rotate integer1 ofRotations integer Rotates the bits in a binary integer You can enter integer1 in any number base it is converted automatically to a signed 32 bit binary form If the magnitude of integer1 is too large for this form a symmetric modulo operation brings it within the range In Bin base mode rotate 0b1111010110000110101...

Page 841: ... round expression1 digits expression Returns the argument rounded to the specified number of digits after the decimal point digits must be an integer in the range 0 12 If digits is not included returns the argument rounded to 12 significant digits Note Display digits mode may affect how this is displayed round 1 234567 3 1 235 round list1 digits list Returns a list of the elements rounded to the s...

Page 842: ...the pixel coordinates of the upper left corner of the picture Default coordinates are 0 0 Note For less than full screen pictures only the area affected by the new picture is cleared rref MATH Matrix menu rref matrix1 tol matrix Returns the reduced row echelon form of matrix1 rref ë 2 ë 2 0 ë 6 1 ë 1 9 ë 9 ë 5 2 4 ë 4 1 0 0 66 71 0 1 0 147 71 0 0 1 ë 62 71 Optionally any matrix element is treated ...

Page 843: ...expression1 or returns a list containing the hyperbolic secants of the list1 elements sech 3 1 cosh 3 sech 1 2 3 4 1 cosh 1 198 1 cosh 4 sechL1 MATH Hyperbolic menu sechL1 expression1 expression sechL1 list1 list Returns the inverse hyperbolic secant of expression1 or returns a list containing the inverse hyperbolic secants of each element of list1 In Radian angle and Rectangular complex mode sech...

Page 844: ...m that allows either a TI 92 Voyage 200 or TI 92 Plus to be used Refer to SendCalc for more information SendChat sends a variable only if that variable is compatible with the TI 92 which is typically true in chat programs However SendChat will not send an archived variable a TI 89 graph data base etc Program segment a b x SendChat x seq MATH List menu seq expression var low high step list Incremen...

Page 845: ...s the name of the current folder as a string and sets newfolderName as the current folder The folder newfolderName must exist newFold chris Done setFold main chris setFold chris oldfoldr main 1 a 1 setFold oldfoldr chris a a chris a 1 setGraph CATALOG setGraph modeNameString settingString string Sets the Graph mode modeNameString to settingString and returns the previous setting of the mode Storin...

Page 846: ...ingString is a character string that specifies the new setting for the mode It must be one of the settings listed below for the specific mode you are setting list contains pairs of keyword strings and will set them all at once This is recommended for multiple mode changes The example shown may not work if each of the pairs is entered with a separate setMode in the order shown Use setMode var to re...

Page 847: ...f the parameter Storing the previous setting lets you restore it later modeNameString is a character string that specifies which parameter you want to set It must be one of the parameters from the table below settingString is a character string that specifies the new setting for the parameter It must be one of the settings listed below for the specific parameter you are setting setTable Graph ì Ta...

Page 848: ...rns a list of the previous defaults To specify the built in SI metric or ENG US system list1 uses the form SI or ENG US To specify a custom set of default units list1 uses the form CUSTOM cat1 unit1 cat2 unit2 where each cat and unit pair specifies a category and its default unit You can specify built in units only not user defined units Any category not specified will use its previous custom unit...

Page 849: ...n specifies one of four shading patterns 1 vertical default 2 horizontal 3 negative slope 45 4 positive slope 45 patRes specifies the resolution of the shading patterns 1 solid shading 2 1 pixel spacing default 3 2 pixels spacing 10 9 pixels spacing Note Interactive shading is available on the Graph screen through the Shade instruction Automatic shading of a specific function is available through ...

Page 850: ...efix zero not the letter O 0b00000000000001111010110000110101 produces 0b00000000000000111101011000011010 The result is displayed according to the Base mode Leading zeros are not shown shift list1 ofShifts list Returns a copy of list1 shifted right or left by ofShifts elements Does not alter list1 If ofShifts is positive the shift is to the left If ofShifts is negative the shift is to the right Th...

Page 851: ... abs x 1 If complex format mode is REAL sign ë 3 0 3 ë 1 1 1 simult MATH Matrix menu simult coeffMatrix constVector tol matrix Returns a column vector that contains the solutions to a system of linear equations coeffMatrix must be a square matrix that contains the coefficients of the equations constVector must have the same number of rows same dimension as coeffMatrix and contain the constants Opt...

Page 852: ...quareMatrix Returns the matrix sine of squareMatrix1 This is not the same as calculating the sine of each element For information about the calculation method refer to cos squareMatrix1 must be diagonalizable The result always contains floating point numbers In Radian angle mode sin 1 5 3 4 2 1 6 ë 2 1 942 ë 045 ë 031 ë 045 949 ë 020 ë 048 ë 005 961 sinê Q key H 2 Q key sinê expression1 expression...

Page 853: ... Radian angle mode sinh 1 5 3 4 2 1 6 ë 2 1 360 954 305 708 239 604 352 912 233 495 193 564 298 632 154 599 140 251 sinhê MATH Hyperbolic menu sinhê expression1 expression sinhê list1 list sinhê expression1 returns the inverse hyperbolic sine of the argument as an expression sinhê list1 returns a list of the inverse hyperbolic sines of each element of list1 sinhê 0 0 sinhê 0 2 1 3 0 1 487 sinhê 3 ...

Page 854: ...1 x Done NewPlot 1 1 L1 L2 Done 9 solve MATH Algebra menu solve equation var Boolean expression solve inequality var Boolean expression Returns candidate real solutions of an equation or an inequality for var The goal is to return candidates for all solutions However there might be equations or inequalities for which the number of solutions is infinite solve aù x 2 bù x c 0 x x bñ 4ø aø c b 2ø a o...

Page 855: ...g an integer in the interval 1 255 Such variables designate an arbitrary integer In Radian angle mode solve sin x 0 x x n1ø p In real mode fractional powers having odd denominators denote only the real branch Otherwise multiple branched expressions such as fractional powers logarithms and inverse trigonometric functions denote only the principal branch Consequently solve produces only solutions co...

Page 856: ...ns might contain arbitrary constants of the form k where k is an integer suffix from 1 through 255 The suffix resets to 1 when you use ClrHome or ƒ 8 Clear Home For polynomial systems computation time or memory exhaustion may depend strongly on the order in which you list solution variables If your initial choice exhausts memory or your patience try rearranging the variables in the equations and o...

Page 857: ...Name2 listName3 SortD vectorName1 vectorName 2 vectorName 3 Identical to SortA except SortD sorts the elements in descending order 2 1 4 3 list1 2 1 4 3 1 2 3 4 list2 1 2 3 4 SortD list1 list2 Done list1 4 3 2 1 list2 3 4 1 2 4Sphere MATH Matrix Vector ops menu vector 4Sphere Displays the row or column vector in spherical form r oq of vector must be of dimension 3 and can be either a row or a colu...

Page 858: ...he corresponding element in matrix1 Note matrix1 must have at least two rows stdDev 1 2 5 3 0 1 5 7 3 2 179 1 014 2 stdDev L1 2 5 3 2 5 7 3 6 L4 4 2 3 3 1 7 2 7005 5 44695 StoGDB CATALOG StoGDB GDBvar Creates a Graph database GDB variable that contains the current Graphing mode Y functions Window variables Graph format settings 1 or 2 Graph setting split screen and ratio settings if 2 Graph mode A...

Page 859: ...ing property stylePropertyString equanum must be an integer from 1 99 and the function must already exist stylePropertyString must be one of Line Dot Square Thick Animate Path Above or Below Note that in parametric graphing only the xt half of the pair contains the style information Valid style names vs graphing mode Function all styles Parametric Polar line dot square thick animate path Sequence ...

Page 860: ...f rows sum 1 2 3 4 5 6 5 7 9 sum 1 2 3 4 5 6 7 8 9 12 15 18 sum 1 2 3 4 5 6 7 8 9 2 3 11 13 15 switch CATALOG switch integer1 integer Returns the number of the active window Also can set the active window Note Window 1 is left or top Window 2 is right or bottom If integer1 0 returns the active window number If integer1 1 activates window 1 and returns the previously active window number If integer...

Page 861: ... starting with 1 The expressions can be modified or individually deleted using the edit functions available when the table is displayed by pressing Header The currently selected functions in the Y Editor are temporarily ignored To clear the functions created by Table or Graph execute the ClrGraph command or display the Y Editor If the var parameter is omitted the current graph mode independent var...

Page 862: ... 835 ë 5 481 36 818 ë 32 806 ë 10 459 tanê S key H 2 S key tanê expression1 expression tanê list1 list tanê expression1 returns the angle whose tangent is expression1 as an expression tanê list1 returns a list of the inverse tangents of each element of list1 Note The result is returned as either a degree or radian angle according to the current angle mode setting In Degree angle mode tanê 1 45 In ...

Page 863: ...inverse hyperbolic tangent of squareMatrix1 This is not the same as calculating the inverse hyperbolic tangent of each element For information about the calculation method refer to cos squareMatrix1 must be diagonalizable The result always contains floating point numbers In Radian angle mode and Rectangular complex format mode tanhê 1 5 3 4 2 1 6 ë 2 1 ë 099 164 øi 267 ì 1 490 øi ë 087 ì 725 øi 47...

Page 864: ...are many possible equivalent results Consequently a result might differ from a result shown in other publications Sometimes tExpand will accomplish your goals when the default trigonometric simplification does not tExpand tends to reverse transformations done by tCollect Sometimes applying tCollect to a result from tExpand or vice versa in two separate steps simplifies an expression Note Degree mo...

Page 865: ...Dropdown Month you were born seq string i i 1 12 Var1 EndDlog tmpCnv CATALOG tmpCnv expression1_ tempUnit1 _ tempUnit2 expression _ tempUnit2 Converts a temperature value specified by expression1 from one unit to another Valid temperature units are _ C Celsius _ F Fahrenheit _ K Kelvin _ R Rankine For example 100_ C converts to 212_ F To convert a temperature range use tmpCnv instead tmpCnv 100_ c...

Page 866: ...tead of a range use tmpCnv Toolbar CATALOG Toolbar block EndTBar Creates a toolbar menu block can be either a single statement or a sequence of statements separated with the character The statements can be either Title or Item Items must have labels A Title must also have a label if it does not have an item Program segment Toolbar Title Examples Item Trig t Item Calc c Item Stop Pexit EndTbar Note...

Page 867: ...ual dimensions except for list5 list1 represents xlist list2 represents ylist list3 represents frequency list4 represents category codes list5 represents category include list Note list1 through list4 must be a variable name or c1 c99 columns in the last data variable shown in the Data Matrix Editor list5 does not have to be a variable name and cannot be c1 c99 0 1 2 3 4 5 6 L1 0 1 2 0 2 3 4 3 4 6...

Page 868: ...n at least two elements variance a b c añ aø b c bñ bø c cñ 3 variance 1 2 5 ë 6 3 ë 2 31 2 variance 1 3 5 4 6 2 68 33 variance matrix1 freqmatrix matrix Returns a row vector containing the variance of each column in matrix1 Each freqmatrix element counts the number of consecutive occurrences of the corresponding element in matrix1 Note matrix1 must contain at least two rows variance 1 2 5 ë 3 0 1...

Page 869: ...wo pieces H ClrGraph Done Graph when x 0 when x ë p 4ù sin x 2x 3 5ì x 2 when is helpful for defining recursive functions when n 0 nù factoral nì 1 1 factoral n Done factoral 3 6 3 6 While CATALOG While condition block EndWhile Executes the statements in block as long as condition is true block can be either a single statement or a sequence of statements separated with the character Program segmen...

Page 870: ... Base mode You can enter the integers in any number base For a binary or hexadecimal entry you must use the 0b or 0h prefix respectively Without a prefix integers are treated as decimal base 10 If you enter a decimal integer that is too large for a signed 32 bit binary form a symmetric modulo operation is used to bring the value into the appropriate range Note See or In Hex base mode 0h7AC36 xor 0...

Page 871: ...wn whose value you seek Optionally you can specify an initial guess for a variable Each varOrGuess must have the form variable or variable real or non real number For example x is valid and so is x 3 If all of the expressions are polynomials and if you do NOT specify any initial guesses zeros uses the lexical Gröbner Buchberger elimination method to attempt to determine all real zeros For example ...

Page 872: ...n any variable but all expressions are linear in the unknowns zeros uses Gaussian elimination to attempt to determine all real zeros zeros x e z ù yì 1 xì yì sin z x y ez øsin z 1 ez 1 ë sin z ì 1 ez 1 If a system is neither polynomial in all of its variables nor linear in its unknowns zeros determines at most one zero using an approximate iterative method To do so the number of unknowns must equa...

Page 873: ...d and displays the Graph screen Note Does not adjust ymin and ymax for histograms In function graphing mode 1 2 3 4 L1 1 2 3 4 2 3 4 5 L2 2 3 4 5 newPlot 1 1 L1 L2 Done ZoomStd H ZoomData ZoomDec CATALOG ZoomDec Adjusts the viewing window so that x and y 0 1 and displays the Graph screen with the origin centered on the screen In function graphing mode 1 25xù cos x y1 x Done ZoomStd H ZoomDec ...

Page 874: ...the Graph screen lets you set a center point for a zoom in and updates the viewing window The magnitude of the zoom is dependent on the Zoom factors xFact and yFact In 3D Graph mode the magnitude is dependent on xFact yFact and zFact In function graphing mode 1 25xù cos x y1 x Done ZoomStd ZoomIn ZoomInt CATALOG ZoomInt Displays the Graph screen lets you set a center point for the zoom and adjusts...

Page 875: ...Prev Displays the Graph screen and updates the viewing window with the settings in use before the last zoom ZoomRcl CATALOG ZoomRcl Displays the Graph screen and updates the viewing window using the settings stored with the ZoomSto instruction ZoomSqr CATALOG ZoomSqr Displays the Graph screen adjusts the x or y window settings so that each pixel represents an equal width and height in the coordina...

Page 876: ...contour 5 Differential equations graphing t 0 10 1 0 x ë 1 10 1 y ë 10 10 1 ncurves 0 Estep 1 diftol 001 fldres 14 dtime 0 In function graphing mode 1 25xù cos x y1 x Done ZoomStd ZoomSto CATALOG ZoomSto Stores the current Window settings in the Zoom memory You can use ZoomRcl to restore the settings ZoomTrig CATALOG ZoomTrig Displays the Graph screen sets x to p 24 and xscl to p 2 centers the ori...

Page 877: ...on1 minus expression2 6ì 2 4 pì pà6 5ø p 6 list1 list2 list matrix1 matrix2 matrix Subtracts each element in list2 or matrix2 from the corresponding element in list1 or matrix1 and returns the results Dimensions of the arguments must be equal 22 p pà2 ì 10 5 pà2 12 pì 5 0 3 4 ì 1 2 2 2 expression list1 list list1 expression list Subtracts each list1 element from expression or subtracts expression ...

Page 878: ... the products of expression and each element in matrix1 Note Use ù dot multiply to multiply an expression by each element 1 2 3 4 ù 01 01 02 03 04 lù identity 3 l 0 0 0 l 0 0 0 l à divide ekey expression1 à expression2 expression Returns the quotient of expression1 divided by expression2 2 3 45 57971 x 3 x x2 list1 à list2 list Returns a list containing the quotients of list1 divided by list2 Dime...

Page 879: ...Matrix1 integer matrix Returns squareMatrix1 raised to the integer power squareMatrix1 must be a square matrix If integer ë 1 computes the inverse matrix If integer ë 1 computes the inverse matrix to an appropriate positive power 1 2 3 4 2 1 2 3 4 ë 1 1 2 3 4 ë 2 dot add keys matrix1 matrix2 matrix expression matrix1 matrix matrix1 matrix2 returns a matrix that is the sum of each pair of correspon...

Page 880: ...atrix matrix1 matrix2 returns a matrix where each element in matrix2 is the exponent for the corresponding element in matrix1 expression matrix1 returns a matrix where each element in matrix1 is the exponent for expression a 2 b 3 c 4 5 d x c 4 5 d ë negate key and MATH Base menu ëexpression1 expression ë list1 list ë matrix1 matrix Returns the negation of the argument For a list or matrix returns...

Page 881: ...f EndFunc Graph g x Á key expression1 expression2 Boolean expression list1 list2 Boolean list matrix1 matrix2 Boolean matrix Returns true if expression1 is determined to be not equal to expression2 Returns false if expression1 is determined to be equal to expression2 Anything else returns a simplified form of the equation For lists and matrices returns comparisons element by element See equal exam...

Page 882: ...less than or equal to expression2 Anything else returns a simplified form of the equation For lists and matrices returns comparisons element by element See equal example key expression1 expression2 Boolean expression list1 list2 Boolean list matrix1 matrix2 Boolean matrix Returns true if expression1 is determined to be greater than or equal to expression2 Returns false if expression1 is determined...

Page 883: ...essions are sometimes added to make an anti derivative valid over a larger interval than the usual formula 1 2ì cos x x tmp x ClrGraph Graph tmp x Graph 1 2ì cos x Graph 3 2tanê 3 tan x 2 3 returns itself for pieces of expression1 that it cannot determine as an explicit finite combination of its built in functions and operators When lower and upper are both present an attempt is made to locate any...

Page 884: ... var high 1 lowì 1 if high lowì 1 Π 1 k k 4 1 6 Π 1 k k 4 1 ù Π 1 k k 2 4 1 4 G sum MATH Calculus menu G expression1 var low high expression Evaluates expression1 for each value of var from low to high and returns the sum of the results G 1 n n 1 5 137 60 G k 2 k 1 n nø n 1 ø 2ø n 1 6 G 1 n 2 n 1 ˆ pñ 6 G expression1 var low lowì 1 0 G k k 4 3 0 G expression1 var low high ë G expression1 var high ...

Page 885: ... expression by p 180 In Degree angle mode returns expression unchanged This function gives you a way to use a degree angle while in Radian mode In Radian angle mode sin cos tan and polar to rectangular conversions expect the angle argument to be in radians In Radian angle mode cos 45 2 2 cos 0 p 4 90 30 12 1 707 0 864 o angle 2 key radius oq_angle vector polar input radius oq_angle Z_coordinate ve...

Page 886: ...q key H 2 q key expression_unit Designates the units for an expression All unit names must begin with an underscore You can use pre defined units or create your own units For a list of pre defined units refer to the module about constants and measurement units You can press 2 9 H À to select units from a menu or you can type the unit names directly 3_m 4 _ft 9 842 ø_ft Note To type 4 press 2 p var...

Page 887: ...e power of the argument For a list returns 10 raised to the power of the elements in list1 10 1 5 31 622 10 0 ë 2 2 a 1 1 100 100 10a 10 squareMatrix1 squareMatrix Returns 10 raised to the power of squareMatrix1 This is not the same as calculating 10 raised to the power of each element For information about the calculation method refer to cos squareMatrix1 must be diagonalizable The result always ...

Page 888: ...val constraints take the form of one or more inequalities joined by logical and operators Interval constraints also permit simplification that otherwise might be invalid or not computable solve x 2ì 1 0 x x 0 and x 2 x 1 x ù 1 x x 0 1 x ù 1 x 1 x ø x Exclusions use the not equals or ƒ relational operator to exclude a specific value from consideration They are used primarily to exclude an exact sol...

Page 889: ...ment Get 10 points from the Graph screen For i 1 10 This loops 10 times 0b 0h µ j B keys H µ B keys µ j H keys H µ H keys 0bbinaryNumber 0hhexadecimalNumber Denotes a binary or hexadecimal number respectively To enter a binary or hex number you must enter the 0b or 0h prefix regardless of the Base mode Without a prefix a number is treated as decimal base 10 Results are displayed according to the B...

Page 890: ...rmation 913 System Variables and Reserved Names 914 EOS Equation Operating System Hierarchy 915 Regression Formulas 917 Contour Levels and Implicit Plot Algorithm 919 Runge Kutta Method 920 Battery Information 921 In Case of Difficulty 924 Texas Instruments TI Support and Service 926 This section contains a comprehensive list of TI 89 Titanium Voyage 200 error messages and character codes It also ...

Page 891: ...ment must be a label name 90 Argument must be a list 100 Argument must be a matrix 110 Argument must be a Pic 120 Argument must be a Pic or string 130 Argument must be a string 140 Argument must be a variable name For example DelVar 12 is invalid because a number cannot be a variable name 150 Argument must be an empty folder name TI 89 Titanium Voyage 200 Error Messages This section lists error me...

Page 892: ...nite replacement of variable values during simplification For example a 1 a where a is an undefined variable will cause this error 200 Constraint expression invalid For example solve 3x 2ì 4 0 x x 0 or x 5 would produce this error message because the constraint is separated by or and not and 205 Data is too big to save to a variable Please use F6 Util to reduce the size The size of the data in the...

Page 893: ...08 Flash application not found 310 First argument of nSolve must be a univariate equation The first argument must be an equation and the equation cannot contain a non valued variable other than the variable of interest For example nSolve 3x 2ì 4 0 x is a valid equation however nSolve 3x 2ì 4 x is not an equation and nSolve 3x 2ì y 0 x is not a univariate equation because y has no value in this exa...

Page 894: ... Screen module 460 Invalid in Custom EndCustm block 470 Invalid in Dialog EndDlog block 480 Invalid in Toolbar EndTBar block 490 Invalid in Try EndTry block 500 Invalid label Label names must follow the same rules used for naming variables 510 Invalid list or matrix For example a list inside a list such as 2 3 4 is not valid 520 Invalid outside Custom EndCustm or ToolBar EndTbar blocks For example...

Page 895: ... cannot contain PIC variables and items must be preceded by a title A Toolbar EndTBar block must have a second argument if no items follow or items must have a second argument and must be preceded by a title 600 Invalid table 605 Invalid use of units 610 Invalid variable name in a Local statement 620 Invalid variable or function name 630 Invalid variable reference 640 Invalid vector syntax 650 Lin...

Page 896: ...y1 x xñ which does not exist this error will be displayed 790 Non algebraic variable in expression If a is the name of a PIC GDB MAC FIG etc a 1 is invalid Use a different variable name in the expression or delete the variable 800 Non real result For example if the unit is in the REAL setting of the Complex Format mode ln ë 2 is invalid 810 Not enough memory to save current variable Please delete ...

Page 897: ... the entry is incorrect For example x ì y x plus minus y is invalid whereas x ë y x plus negative y is correct 930 Too few arguments The expression or equation is missing one or more arguments For example d f x is invalid whereas d f x x is the correct syntax 940 Too many arguments The expression or equation contains an excessive number of arguments and cannot be evaluated 950 Too many subscripts ...

Page 898: ...duce false equation Warning Expected finite real integrand Warning May not be fully simplified Warning More solutions may exist Warning May introduce false solutions Warning Operation may lose solutions Warning Requires returns 32 bit value Warning Overflow replaced by ˆ or ë ˆ Warning Questionable accuracy Warning Questionable solution Warning Solve may specify more zeros Warning Trig argument to...

Page 899: ...mal settings affect only how results are displayed you can enter a number in any format Internally the TI 89 Titanium Voyage 200 retains decimal numbers with 14 significant digits For display purposes such numbers are rounded to a maximum of 12 significant digits 1 FIX 0 2 FIX 1 D FIX 12 Results are always displayed with the selected number of decimal places E FLOAT The number of decimal places va...

Page 900: ...NEERING Similar to scientific notation However The number may have one two or three digits before the decimal The power of 10 exponent is a multiple of three For example 12 34567E3 means 12 34567 103 Note If you select NORMAL but the answer cannot be displayed in the number of digits selected by Display Digits the TI 89 Titanium Voyage 200 displays the answer in SCIENTIFIC notation If Display Digi...

Page 901: ...layed in conventional mathematical format For example p2 p 2 or xì3 x Note For a complete description of these settings refer to Formats of Displayed Results in the Operating the Calculator module Lets you split the screen into two parts For example you can display a graph and see the Y Editor at the same time 1 FULL The screen is not split 2 TOP BOTTOM The applications are shown in two screens th...

Page 902: ...art of the split screen and Graph 2 sets the bottom or right part The available choices are the same as for Graph Specifies the proportional sizes of the two parts of a split screen 1 1 The screen is split evenly 1 2 The bottom or right part is approximately twice the size of the top or left part 2 1 The top or left part is approximately twice the size of the bottom or right part Specifies how fra...

Page 903: ...fined units 1 SI Select SI for the metric system of measurements 2 ENG US Select ENG US for the non metric system of measurements 3 CUSTOM Allows you to select custom defaults Lets you select custom defaults This mode is dimmed until you select Unit System 3 CUSTOM Lets you localize the TI 89 Titanium Voyage 200 into one of several languages depending on which language Flash applications are insta...

Page 904: ...ars when you Press O Turn the unit on after it has been turned off by pressing 2 Press 2 K from an App that is displayed in full screen mode OFF Does not display the navigable Apps desktop The unit defaults to the calculator Home screen The calculator Home screen displays when you press 2 K The APPLICATIONS menu displays when you press O Apps Desktop ...

Page 905: ... ρ 142 Σ 143 σ 144 τ 145 φ 146 ψ 147 Ω 148 ω 149 E 150 e 151 i 152 r 153 î 154 ü 155 ý 156 c 157 ƒ 158 159 o 160 161 162 163 164 165 166 167 168 169 170 a 171 172 173 174 175 176 177 178 ñ 179 ò 180 ê 181 µ 182 183 ø 184 185 186 o 187 188 d 189 190 ˆ 191 192 À 193 Á 194 Â 195 Ã 196 Ä 197 Å 198 Æ 199 Ç 200 È 201 É 202 Ê 203 Ë 204 Ì 205 Í 206 Î 207 Ï 208 Ð 209 Ñ 210 Ò 211 Ó 212 Ô 213 Õ 214 Ö 215 216...

Page 906: ...ATLG 278 CATLG 278 i 151 190 CATLG 278 0 BS 257 BS 257 INS 4353 DEL 8449 BS 257 M CLEAR 263 CLEAR 263 CLEAR 263 8455 CLEAR 263 Ù x 120 X 88 LN 4184 e x 8280 x 120 Ú y 121 Y 89 SIN 4185 SIN 1 8281 y 121 Û z 122 Z 90 COS 4186 COS 1 8282 z 122 Ü t 116 T 84 TAN 4180 TAN 1 8276 t 116 Z 94 94 π 140 θ 136 94 Í 124 F 70 176 Format d b 8316 f 102 c 40 B 66 123 b 98 d 41 C 67 125 169 c 99 b 44 D 68 91 8236 ...

Page 907: ...v 118 1 49 Q 81 34 8241 q 113 2 50 R 82 92 8242 r 114 ª 3 51 S 83 UNITS 4147 8243 s 115 y 4 52 L 76 58 8244 l 108 z 5 53 M 77 MATH 4149 8245 m 109 6 54 N 78 MEM 4150 8246 n 110 m 7 55 G 71 4151 8247 g 103 n 8 56 H 72 d 4152 8248 h 104 o 9 57 I 73 59 8249 i 105 Table 2 Arrow Keys including diagonal movement Key Normal 2 j C 338 16722 4434 8530 33106 B 340 16724 4436 8532 33108 D 344 16728 4440 8536...

Page 908: ...ek Letters prefixed by c Keys Second modifier j Assoc Value Assoc Value Á A α 128 c B β 129 b D δ 133 132 e E ε 134 Í F φ 145 m G γ 131 Γ 130 y L λ 137 z M µ 181 P π 140 Π 139 R ρ 141 ª S σ 143 Σ 142 Ü T τ 144 W ω 148 Ω 147 Ù ξ 138 Ú ψ 146 Û ζ 135 ...

Page 909: ...WITCH 4361 8457 CR 13 CR 13 ENTRY 4109 APPROX 8205 W SIN 259 SIN 259 SIN 1 4355 8451 X COS 260 COS 260 COS 1 4356 8452 Y TAN 261 TAN 261 TAN 1 4357 8453 Z 94 94 p 140 8286 c 40 40 123 8232 d 41 41 125 8233 b 44 44 91 8236 e 47 47 93 8239 p 42 42 4138 8234 45 45 VAR LNK 4141 Contrast ì 43 43 CHAR 4139 Contrast STO4 258 STO4 258 RCL 4354 8450 SPACE 32 32 32 8224 Á 61 61 92 8253 0 BS 257 BS 257 INS 4...

Page 910: ...58 C c 99 C 67 Table 4 COPY 8259 D d 100 D 68 176 8260 E e 101 E 69 Table 5 WINDOW 8261 F f 102 F 70 159 FORMAT 8262 G g 103 G 71 Table 6 8263 H h 104 H 72 38 8264 I i 105 I 73 i 151 8265 J 106 J 74 190 8266 K k 107 K 75 124 KEY 8267 L l 108 L 76 34 8268 M m 109 M 77 59 8269 N n 110 N 78 Table 7 NEW 8270 O o 111 O 79 Table 8 OPEN 8271 P p 112 P 80 _ 95 UNITS 8272 Q q 113 Q 81 63 CALCHOME 8273 R r ...

Page 911: ... 4438 8534 33110 D and A 345 16729 4441 8537 33113 D and B 348 16732 4444 8540 33116 Note The Grab modifier only affects the arrow keys Table 3 Grave Accent Letters prefixed by 2 A Key Assoc Normal A à 224 192 E è 232 200 I ì 236 204 O ò 242 210 U ù 249 217 Table 4 Cedilla Letters prefixed by 2 C Key Assoc Normal C ç 231 199 Table 5 Acute Accent Letters prefixed by 2 E Key Assoc Normal A á 225 193...

Page 912: ... ρ 141 S σ 143 142 T τ 144 W ω 148 147 X ξ 138 Y ψ 146 Z ζ 135 Table 7 Tilde Letters prefixed by 2 N Key Assoc Normal N ñ 241 209 O õ 245 Table 8 Caret Letters prefixed by 2 O Key Assoc Normal A â 226 194 E ê 234 202 I î 238 206 O ô 244 212 U û 251 219 Table 9 Umlaut Letters prefixed by 2 U Key Assoc Normal A ä 228 196 E ë 235 203 I ï 239 207 O ö 246 214 U ü 252 220 Y ÿ 255 ...

Page 913: ...se the form When the Angle mode setting is a bi Radian or Degree reiq Radian only In Degree angle mode this form causes a Domain error roq Radian or Degree Use the following methods to enter a complex number To enter the Do this Rectangular form a bi Substitute the applicable values or variable names for a and b a b 2 For example Imaginary Real Entering Complex Numbers You can enter complex number...

Page 914: ...uch as cFactor cSolve or cZeros If complex results are displayed they will be shown in either a bi or reiq form RECTANGULAR Displays complex results as a bi POLAR Displays complex results as reiq if the Angle mode Radian or roq if the Angle mode Degree Important Do not use the reiq polar form in Degree angle mode It will cause a Domain error Note To get the e symbol press TI 89 Titanium s Voyage 2...

Page 915: ...n angle mode is recommended for complex number calculations Internally the TI 89 Titanium Voyage 200 converts all entered trig values to radians but it does not convert values for exponential logarithmic or hyperbolic functions In Degree angle mode complex identities such as e iq cos q i sin q are not generally true because the values for cos and sin are converted to radians while those for e are ...

Page 916: ...s calculated as xmax ì xmin of x pixels ì 1 If x is entered from the Home screen or a program xmax is calculated as xmin x ù of x pixels ì 1 The Window variable ymin is the center of the bottom pixel used and ymax is the center of the top pixel used y is the distance between the centers of two vertically adjacent pixels y is calculated as ymax ì ymin of y pixels ì 1 If y is entered from the Home s...

Page 917: ...p zt0de ztmaxde ztstepde ztplotde zzmin zzmax zzscl zeyeq zeyef zeyeψ znmin znmax zpltstrt zpltstep x y Gx sx Gx2 Gxy Gy sy Gy2 corr maxX maxY medStat medx1 medx2 medx3 medy1 medy2 medy3 minX minY nStat q1 q3 regCoef regEq x seed1 seed2 Sx Sy R2 tblStart tbl tblInput c1 c99 sysData main ok errornum eqn exp System Variables and Reserved Names This section lists the names of system variables and res...

Page 918: ... The number of opening and closing parentheses brackets and braces must be the same within an expression or equation If not an error message is displayed that indicates the missing element For example 1 2 3 4 will display the error message Missing Note Because the TI 89 Titanium Voyage 200 allows you to define your own functions a variable name followed by an expression in parentheses is considere...

Page 919: ...o yield 4096 Exponentiation and element by element exponentiation are evaluated from right to left For example the expression 2 3 2 is evaluated the same as 2 3 2 to produce 512 This is different from 2 3 2 which is 64 To enter a negative number press followed by the number Post operations and exponentiation are performed before negation For example the result of ëx2 is a negative number and ë92 ë...

Page 920: ...al expression is a sin bxi c dì yi For SinReg therefore the least squares algorithm finds the constants a b c and d that minimize the function J a bx c d y i i i N sin 2 1 Regression Description CubicReg Uses the least squares algorithm to fit the third order polynomial y ax3 bx2 cx d For four data points the equation is a polynomial fit for five or more it is a polynomial regression At least four...

Page 921: ...Reg Uses the least squares algorithm and transformed values ln x and ln y to fit the model equation y axb QuadReg Uses the least squares algorithm to fit the second order polynomial y ax2 bx c For three data points the equation is a polynomial fit for four or more it is a polynomial regression At least three data points are required QuartReg Uses the least squares algorithm to fit the fourth order...

Page 922: ...ive points shown to the right the difference between the point s z value and the contour value is calculated A sign change between any two adjacent points implies that a contour crosses the line that joins those two points Linear interpolation is used to approximate where the zero crosses the line Within the rectangle any zero crossings are connected with straight lines This process is repeated fo...

Page 923: ...nary Differential Equations by L F Shampine New York Chapman Hall 1994 The TI 89 Titanium Voyage 200 software does not adjust the step size to land on particular output points Rather it takes the biggest steps that it can based on the error tolerance diftol and obtains results for xn c x c xn 1 using the cubic interpolating polynomial passing through the point xn yn with slope F1 and through xn 1 ...

Page 924: ...or allow them to run down completely you can change either type of battery without losing anything in memory Take these precautions when replacing batteries Do not leave batteries within the reach of children Do not mix new and used batteries Do not mix brands or types within brands of batteries Do not mix rechargeable and non rechargeable batteries Install batteries according to polarity and diag...

Page 925: ...nd diagram inside the battery compartment 6 Replace the battery cover by inserting the two prongs into the two slots at the bottom of the battery compartment and then push the cover until the latch snaps closed To replace the lithium backup battery remove the battery cover and unscrew the tiny screw holding the BACK UP BATTERY cover in place Remove the old battery and install a new WR44SW or 303 b...

Page 926: ... inside the battery compartment 6 Slide the battery cover onto the device prong side first Gently push the cover until the prongs snap into place To replace the lithium backup battery remove the battery cover Insert a blunt object into the circular indentation next to the battery Gently place a finger on the lithium battery and pry the battery out Slide in a new CR1616 or CR1620 battery positive s...

Page 927: ...or is displayed A graph or program is paused and the TI 89 Titanium Voyage 200 is waiting for input press An error message is displayed Refer to the list of error messages in this module Press Nto clear The TI 89 Titanium Voyage 200 does not appear to be working properly Press Nseveral times to exit any menu or dialog box and to return the cursor to the entry line or Be sure that the batteries are...

Page 928: ...as you reinstall the battery 3 Continue holding and dfor five seconds before releasing The Voyage 200 appears to be locked up and will not respond to keyboard input The following action clears RAM This erases all data programs and user defined variables functions or folders Press and hold 2 and Then press and release The following action clears RAM and Flash ROM This erases all data programs user ...

Page 929: ...PF UWRRQTV D G OCKN GFWECVKQP VK EQO UWRRQTV 2JQPG PQV VQNN HTGG WUVQOGTU KP VJG 7 5 CPCFC GZKEQ 2WGTVQ 4KEQ CPF 8KTIKP UNCPFU NYC U EQPVCEV 6GZCU PUVTWOGPVU WUVQOGT 5WRRQTV DGHQTG TGVWTPKPI C RTQFWEV HQT UGTXKEG NN QVJGT EWUVQOGTU 4GHGT VQ VJG NGCHNGV GPENQUGF YKVJ VJKU RTQFWEV JCTFYCTG QT EQPVCEV QWT NQECN 6GZCU PUVTWOGPVU TGVCKNGT FKUVTKDWVQT 6GZCU PUVTWOGPVU 5WRRQTV CPF 5GTXKEG QT IGPGTCN KPHQ...

Page 930: ...hen switch to the Italian Language mode the program will produce an error To avoid this error you must substitute digits for the alpha characters These digits operate in all languages This appendix contains the digit substitutions for these strings The following examples show how to substitute digits in the setMode function Example 1 A program using alpha parameter mode strings setMode Graph Seque...

Page 931: ...IC 2 POLAR 3 SEQUENCE 4 3D 5 DIFF EQUATIONS 6 DisplayDigits 2 FIX 0 1 FIX 1 2 FIX 2 3 FIX 3 4 FIX 4 5 FIX 5 6 FIX 6 7 FIX 7 8 FIX 8 9 FIX 9 10 FIX 10 11 FIX 11 12 FIX 12 13 FLOAT 14 FLOAT 1 15 FLOAT 2 16 FLOAT 3 17 FLOAT 4 18 FLOAT 5 19 FLOAT 6 20 FLOAT 7 21 FLOAT 8 22 FLOAT 9 23 setMode and getMode ...

Page 932: ...ial Format 4 NORMAL 1 SCIENTIFIC 2 ENGINEERING 3 Complex Format 5 REAL 1 RECTANGULAR 2 POLAR 3 Vector Format 6 RECTANGULAR 1 CYLINDRICAL 2 SPHERICAL 3 Pretty Print 7 OFF 1 ON 2 SplitScreen 8 FULL 1 TOP BOTTOM 2 LEFT RIGHT 3 Split1App 9 applications are not numbered Split2App 10 applications are not numbered Number of Graphs 11 1 1 2 2 ...

Page 933: ...uide 930 Parameter Mode Setting Strings Graph 2 12 FUNCTION 1 PARAMETRIC 2 POLAR 3 SEQUENCE 4 3D 5 DIFF_EQUATIONS 6 Split Screen Ratio 13 1 1 1 1 2 2 2 1 3 Exact Approx 14 AUTO 1 EXACT 2 APPROXIMATE 3 Base 15 DEC 1 HEX 2 BIN 3 ...

Page 934: ... Coordinates 1 RECT 1 POLAR 2 OFF 3 Graph Order 2 SEQ 1 SIMUL 2 Grid 3 OFF 1 ON 2 Axes 4 In 3D Mode OFF 1 AXES 2 BOX 3 Not in 3D Mode OFF 1 ON 2 Leading Cursor 5 OFF 1 ON 2 Labels 6 OFF 1 ON 1 Seq Axes 7 TIME 1 WEB 2 Custom 3 Solution Method 8 RK 1 EULER 2 setGraph ...

Page 935: ...32 Parameter Mode Setting Strings Fields 9 SLPFLD 1 DIRFLD 2 FLDOFF 3 DE Axes 10 TIME 1 Y1 VS Y2 2 T VS Y 3 Y VS Y 4 Y1 VS Y2 5 Y1 VS Y2 6 XR Style 11 WIRE FRAME 1 HIDDEN SRUFACE 2 CONTOUR LEVELS 3 WIRE AND CONTOUR 4 IMPLICIT PLOT 5 ...

Page 936: ...Appendix C Programmer s Guide 933 Parameter Mode Setting Strings Graph Table 1 OFF 1 ON 2 Independent 2 AUTO 1 ASK 2 Axes 4 setTable ...

Page 937: ...un programs kbdprgm1 through kbdprgm9 p append On screen keyboard map Turn off unit so that it returns to current application the next time you turn it on µ zero c Copy graph coordinates to Home screen history Alpha Rules j Type one lowercase letter Type one uppercase letter 2 Lowercase alpha lock j Uppercase alpha lock j Exit alpha lock 3D Graphing C D A B Animate graph Change animation speed X Y...

Page 938: ...ove cursor to far left 2 B Move cursor to far right C D Scroll tall objects in history 2 C 2 D Page up and page down X Cut C Copy V Paste 3D Graphing C D A B Animate graph Change animation speed X Y Z View along axis µ zero Return to original view F Change graph format style p Expanded normal view Accent Marks 2 A letter à è ì ò ù À È Ì Ò Ù 2 C letter ç Ç 2 E letter á é í ó ú ý Á É Í Ó Ú Ý 2 N let...

Page 939: ...T X Y Z T X Y Z Several lowercase letters 2 End several lowercase letters j Several uppercase letters 2 End several uppercase letters j 2 FUNCTION KEYS F6 2 ˆ ˆ F7 2 F8 2 Š Š NAVIGATION Scroll tall objects up or down in history C D C D Move cursor far left or far right on entry line 2 A 2 B 2 A 2 B Diagonal movement C and A C and B D and A D and B C and A C and B D and A D and B FUNCTIONS Display ...

Page 940: ...b D Greek characters c j or c G or G Keyboard map Place data in Home screen history H Grave à è ì ò ù 2 5 2 A a e i o u Cedilla ç 2 5 6 2 C c Acute á é í ó ú ý 2 5 2 E a e i o u y Tilde ã ñ õ 2 5 6 2 N a n o Caret â ê î ô û 2 5 2 O a e i o u Umlaut ä ë ï ö ü ÿ 2 5 2 U a e i o u y Question mark 2 3 2 Q β Beta 2 5 6 2 S Indirection 2 3 2 T Append p times 2 H Arbitrary 2 R Not equal to symbol Á 2 V F...

Page 941: ...877 subtract 874 angle 882 dot multiplication 877 dot addition 876 dot subtraction 876 dot division 877 dot power 877 divide 875 less than 588 878 insufficient display memory 217 equal 588 878 greater than 588 879 negation key 11 arbitrary integer 263 list list difference 811 tbl table increment 441 tmpCnv temperature range conversion 272 863 x window variable 311 y window variable 311 power 876 _...

Page 942: ...cylindrical vector 780 4DD display as decimal angle 782 4Dec display as decimal integer 665 782 4DMS display as degree minute second 788 4Hex display as hexadecimal 665 804 4Polar display as polar vector 827 4Rect display as rectangular vector 835 4Sphere display as spherical vector 854 7 shift modifier key description 10 status 34 8 diamond modifier key description 10 status 34 8 S SAVE COPY AS e...

Page 943: ...icture 765 Angle mode 175 291 897 angle mode 15 status 34 angle angle 765 angle 882 ans last answer 766 answer last ans 208 APD Automatic Power Down 134 APD Automatic Power Down feature during calculation or program 5 turning on after 5 append 586 880 APPLICATIONS menu 169 APPLICATIONS menu O 45 53 approx approximate 766 Approximate mode 154 176 191 228 approximate approx 243 Apps calculator softw...

Page 944: ...ation 230 automatic tables 444 auto paste 23 200 209 avgRC average rate of change 767 axes sequence CUSTOM 349 Axes graph format 302 401 420 421 Axes settings 372 380 B backspace 0 13 Base mode 15 176 BATT message 191 batteries 136 191 precautions 66 prolonging life 5 replacing 1 63 64 binary display 4Bin 665 767 indicator 0b 886 rotate rotate 670 shift shift 671 BldData build data 425 581 768 Boo...

Page 945: ...9 categories All 28 Apps desktop 29 customizing 29 English 28 example of editing 30 Graphing 28 Math 28 Organizr organizer 28 Science 28 selecting 28 selecting empty 29 SocialSt social studies 28 CBL get return Get 799 programs 617 send list variable Send 840 statistical data 553 554 CBL 2 system activity 740 connecting 62 programs 740 CBR get return Get 799 programs 617 send list variable Send 84...

Page 946: ...661 I O ClrIO 560 604 clipboard 200 637 Clock dialog box 37 operation 36 turning off 42 turning on 44 ClockOff turning clock off 769 ClockOn turning clock on 770 ClrDraw clear drawing 614 770 ClrErr clear error 620 770 ClrGraph clear graph 611 661 770 ClrHome clear home 25 771 ClrIO clear I O 771 ClrIO clear I O 560 604 771 cobweb plot See web plots colDim matrix column dimension 771 colNorm matri...

Page 947: ... 581 687 CopyVar copy variable 687 772 cos cosine 773 cos arccosine 773 cosh hyperbolic cosine 774 cosh hyperbolic arccosine 774 cot cotangent 774 cot inverse cotangent 775 coth hyperbolic cotangent 775 coth inverse hyperbolic cotangent 775 crossP cross product 775 csc cosecant 775 csc inverse cosecant 776 csch hyperbolic cosecant 776 csch inverse hyperbolic cosecant 776 cSolve complex solve 227 7...

Page 948: ...227 244 780 D d first derivative 73 234 252 254 782 darker lighter 135 data new NewData 818 data filtering 736 data plots 106 Data Matrix Editor cell width 512 column header 513 516 517 518 filling 510 list variable 505 507 new NewData 581 scrolling 510 shift shift 847 sorting columns 520 statistical plots 536 values 508 509 data matrix editor 454 date reset 44 setting 36 dayOfWk day of week 782 D...

Page 949: ...quations DIRFLD direction field 401 409 first order 411 430 FLDOFF field off 401 410 437 graphing 396 438 initial conditions 407 second order 413 430 SLPFLD slope field 401 409 434 solution methods 400 425 third order 417 troubleshooting 433 diftol window variable 404 dim dimension 787 dimension dim 586 direction field DIRFLD 401 409 436 DIRFLD direction field 401 409 436 Disp display I O screen 1...

Page 950: ...473 616 788 line Line 615 810 lines 477 479 on a graph 613 parametric DrawParm 472 616 789 Pencil 476 polar DrawPol 472 616 789 slope DrawSlp 480 615 789 tangent line LineTan 616 810 vertical line LineVert 616 810 DrawInv draw inverse 473 616 788 DrawParm draw parametric 472 616 789 DrawPol draw polar 472 616 789 DrawSlp draw slope 480 615 789 drop down menu DropDown 606 DropDown drop down menu 60...

Page 951: ...olving 650 654 658 659 error conditions after APD 5 errors and troubleshooting Circular definition 580 clear error ClrErr 620 770 Memory error 697 698 Out of memory 260 pass error PassErr 620 826 programs 619 transmission 705 715 Estep window variable 404 Euler method 400 425 evaluate polynomial polyEval 827 EXACT mode status 34 exact exact 792 Exact Approx mode 154 176 191 226 228 229 exact appro...

Page 952: ...rner problem 721 population 106 predator prey model 357 421 prime factors 68 programming 115 118 621 Pythagorean theorem 721 quadratic formula 723 rational factors 752 real factors 752 reducing expressions 71 sampling 753 second order differential equation 413 430 sequence graphing 87 solving linear equations 72 247 split screen 102 743 standard annuity 748 statistics 106 symbolic manipulation 73 ...

Page 953: ...ctor factor 70 227 243 246 725 752 factorial 69 879 factoring 246 activity 752 false message 262 family of curves 464 Fibonacci sequence 359 field off FLDOFF 401 410 437 field picture fldpic 405 Fill matrix fill 796 Flash applications 169 183 260 673 674 677 deleting 705 FLASH APPLICATIONS 8 O accessing Apps not listed 54 description 45 key command 13 Flash upgrading operating system 711 712 FLDOF...

Page 954: ...cation 233 graphing 288 maximum fMax 227 253 797 minimum fMin 227 253 797 multistatement 462 off FnOff 297 611 797 on FnOn 297 611 797 part fPart 799 program function Func 572 799 user defined 184 211 258 364 460 462 570 572 783 G Garbage collection message 693 694 695 696 gcd greatest common divisor 799 get time zone GetTmZn 803 Get get return CBL CBR value 553 618 799 get return calculator GetCa...

Page 955: ...graph 804 graph Graph 295 458 465 612 Graph Table table graph 441 graphing category 28 graphs number of 57 58 graphs and graphing f x dx 317 320 3D 361 395 animation 485 Arc 317 323 332 339 clearing ClrGraph 460 611 661 770 contour plots 382 386 387 coordinates 78 305 custom axes 349 custom plots 343 420 421 Derivatives 317 320 332 339 differential equations 396 438 Distance 317 321 332 339 drawin...

Page 956: ... graph database StoGDB 613 855 style Style 612 856 Tangent 317 322 332 339 text 481 time plots 343 349 420 421 trace Trace 307 612 730 740 742 745 863 tracing 78 307 310 332 339 348 367 406 two graph mode 467 468 469 491 Value 317 318 332 339 348 368 406 viewing window 299 329 337 345 365 web plots 343 349 350 window variables 299 329 337 345 365 Y editor 77 80 291 329 335 342 363 398 456 Zero 317...

Page 957: ...5 If if 805 if If 463 567 590 591 imag imaginary part 806 implicit plots 390 393 implied multiplication 148 336 Independent AUTO ASK independent auto ask 444 449 independent auto ask Independent AUTO ASK 442 444 449 indirection 586 881 infinity 263 Inflection graph math tool 317 321 initial conditions 407 initial startup 2 input string InputSt 585 603 708 807 Input input 806 input Input 603 612 In...

Page 958: ...3 600 Labels graph format 302 Language mode 177 language mode changing mode setting 16 viewing 15 last answer 141 152 205 208 last entry 141 205 206 Lbl label 808 lcm least common multiple 808 Leading Cursor graph format 302 least common multiple lcm 808 left left 809 left left 244 586 left right split screen setting 54 setting initial Apps 56 status 32 less than or equal 879 less than or equal 58...

Page 959: ...3 list to matrix list4mat 811 matrix to list mat4list 815 maximum max 815 mid string mid 816 minimum min 816 new data NewData 581 818 new newList 819 operations 760 product product 828 sort ascending SortA 854 sort descending SortD 854 summation sum 837 857 table variables 451 variables 501 ln natural logarithm 811 LnReg logarithmic regression 532 812 local variable Local 574 579 581 582 Local loc...

Page 960: ...maximum max 815 minimum min 816 new data NewData 581 818 new newMat 819 operations 761 pretty print 504 product product 828 QR factorization QR 832 random randMat 726 834 reduced row echelon form rref 249 839 row addition rowAdd 838 row dimension rowDim 838 row echelon form ref 836 row multiplication and addition mRowAdd 817 row norm rowNorm 839 row operation mRow 817 row swap rowSwap 839 submatri...

Page 961: ...tract 244 FLASH APPLICATIONS 8 O 13 45 54 MATH 317 options 10 selecting options 45 submenu options 47 toolbar 163 218 Trig 244 using 163 messages BATT 191 false 262 Garbage collection 693 694 695 696 insufficient display memory 217 true 262 undef undefined 264 mid mid string 816 mid string mid 587 min minimum 816 Minimum graph math tool 78 317 319 minute notation 883 mod modulo 817 modes 173 3D th...

Page 962: ...L polar 34 Pretty Print 15 154 176 RAD radian 34 SEQ sequence 34 setting in programs 600 setting setMode 601 612 843 settings 14 Split App 176 Split Screen 176 split screen 3 15 27 32 34 54 56 58 59 Unit System 177 unit system 15 Vector Format 176 vector format 15 modifier keys 2 8 7 1 10 status 34 move variable MoveVar 581 MoveVar move variable 817 mRow matrix row operation 817 mRowAdd matrix row...

Page 963: ...solution 243 822 number bases 664 Boolean operations 668 conversions 665 math operations 666 Number of Graphs mode 176 numbers irrational 227 228 negative 144 rational 227 228 229 numeric derivative nDeriv 253 818 integral nInt 253 820 solution nSolve 243 822 numeric keypad 11 numeric solver 650 654 658 659 equations 650 652 653 graphing 659 660 661 split screens 660 662 variables 654 658 O on off...

Page 964: ...Pic 582 613 819 recall RclPic 613 835 replace RplcPic 613 839 storing StoPic 613 856 piecewise functions 460 pixel change PxlChg 615 830 circle PxlCrcl 615 830 horizontal line PxlHorz 616 830 line PxlLine 481 615 830 off PxlOff 615 831 on PxlOn 481 615 831 test pxlTest 615 831 text PxlText 615 831 vertical line PxlVert 616 831 plots clearing 539 data 106 new NewPlot 541 612 820 off PlotsOff 297 61...

Page 965: ...8 product Π 253 881 Program Editor 26 programs and programming 18 557 628 arguments 569 assembly language 625 628 branching 567 590 593 calling another program 576 CBL 617 CBL 2 system 740 CBR 617 CBR system 740 clear error ClrErr 620 770 clear graph ClrGraph 460 611 770 clear home ClrHome 771 clear I O ClrIO 560 604 771 clear table ClrTable 771 comment 566 886 conditional tests 587 copying 564 cu...

Page 966: ...t return folder getFold 601 801 get return from calculator GetCalc 618 708 799 get return key getKey 603 801 get return mode getMode 601 802 get return units getUnits 803 go to Goto 578 593 600 804 graphs 611 if If 463 567 590 591 805 input 559 567 603 input Input 603 612 806 label Lbl 578 593 600 808 local Local 574 579 581 582 812 loop Loop 598 814 looping 567 595 597 menu item Item 606 608 808 ...

Page 967: ...ion QR 832 QR QR factorization 832 quadratic regression QuadReg 532 832 QuadReg quadratic regression 532 832 quartic regression QuartReg 533 833 QuartReg quartic regression 533 833 QuickCenter 310 Quit 2 K 14 R R radian 882 R4Pθ polar coordinate 833 R4Pr polar coordinate 834 RAD radian mode 34 radian R 882 rand random number 834 randMat random matrix 726 834 randNorm random norm 834 random matrix ...

Page 968: ...ture RplcPic 613 839 Request request 836 request Request 604 606 results 21 return See get return Return return 837 return Return 463 574 577 right right 837 right right 244 587 rotate rotate 670 837 rotate rotate 587 670 round round 838 row echelon form ref 836 rowAdd matrix row addition 838 rowDim matrix row dimension 838 rowNorm matrix row norm 839 rowSwap matrix row swap 839 RplcPic replace pi...

Page 969: ...ode set mode 601 612 843 setTable set table 444 601 844 setTime set time 844 setTmFmt set time format 844 setTmZn set time zone 845 setUnits set units 601 845 Shade graph math tool 318 323 Shade shade 616 846 shade Shade 616 Shift modifier key 7 description 10 status 34 shift shift 518 587 671 847 shift shift 587 671 show statistical results ShowStat 533 848 ShowStat show statistical results 533 8...

Page 970: ...p 27 selecting active App 58 setting 54 setting initial Apps 56 specifying Apps displayed 56 Split 1 App 56 Split 2 App 56 status 32 status and open Apps 3 viewing 15 square root 881 standard annuity activity 748 standard deviation stdDev 855 start timer startTmr 854 startTmr start timer 854 statistics 525 556 Box Plot 541 Calculation Type 526 531 categories 550 Category 526 528 combinations nCr 8...

Page 971: ...ure StoPic 613 856 symbol 581 885 string expression to string 587 856 strings append 586 880 character code ord 587 character string char 586 769 dimension dim 586 expression to string string 587 856 format format 586 604 611 798 indirection 586 881 inputting InputSt 585 603 708 left left 586 809 mid string mid 587 816 operations 585 586 763 right right 587 837 rotate rotate 587 837 shift shift 58...

Page 972: ...9 tan arctangent 859 Tangent graph math tool 317 322 332 339 tangent tan 859 tanh hyperbolic tangent 859 tanh hyperbolic arctangent 860 Taylor polynomial taylor 253 256 860 taylor Taylor polynomial 860 tblStart table start 441 tCollect trigonometric collection 861 temperature conversion tmpCnv 272 862 temperature range conversion tmpCnv 272 temperature range conversion tmpCnv 863 tExpand trigonome...

Page 973: ...5 863 top bottom split screen setting 54 setting initial Apps 56 status 32 tplot window variable 403 Trace trace 730 740 742 745 863 trace Trace 307 612 730 740 742 745 tracing 78 307 310 332 339 348 367 406 transmitting See linking and transmitting transpose T 858 Trig menu 244 trigonometric collection tCollect 244 expansion tExpand 244 trigonometric collection tCollect 861 trigonometric expansio...

Page 974: ...ystem OS 711 712 user defined functions 184 211 258 364 460 462 570 572 783 user defined units 276 V Value graph math tool 317 318 339 368 406 variables 35 185 187 archiving and unarchiving 691 archiving Archive 581 692 766 clearing 663 copy CopyVar 581 687 772 copying 687 data 502 defined 223 655 delayed simplification 233 delete DelVar 225 257 581 584 784 deleting 705 in applications 689 690 loc...

Page 975: ...lation 355 WEB 343 349 350 WEB web plots 343 349 350 when when 865 when when 460 While while 866 while While 597 Window Editor 53 window variables diftol 404 dtime 404 Estep 404 eyeφ z axis 364 373 375 eyeθ x axis 364 373 375 eyeψ rotation 364 373 375 fldres 404 ncontour 365 ncurves 403 nmax 345 nmin 345 plotStep 345 plotStrt 345 qmax 329 qmin 329 qstep 330 t0 402 tmax 337 402 tplot 403 tstep 337 ...

Page 976: ...03 ymin window variable 299 330 337 345 365 403 yscl window variable 300 330 338 345 403 Z Zero graph math tool 317 319 zeroes activity 745 zeroes zeroes 227 243 250 zeroes zeros 723 868 zeros zeroes 723 868 zmax window variable 365 zmin window variable 365 zoom box ZoomBox 311 313 869 data ZoomData 312 870 decimal ZoomDec 311 870 factors 312 314 fit ZoomFit 312 871 in ZoomIn 311 314 871 integer Z...

Page 977: ...974 ZoomInt zoom integer 871 ZoomOut zoom out 872 ZoomPrev zoom previous 872 ZoomRcl zoom recall 872 ZoomSqr zoom square 872 ZoomStd zoom standard 873 ZoomSto zoom store 873 ZoomTrig zoom trig 873 ...

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