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208

Chapter 15: Equation Solving

15EQSOLV.DOC TI-86, Chap 15, US English Bob Fedorisko Revised: 02/13/01 2:34 PM Printed: 02/13/01 3:04 PM Page 208 of 12

The Solver ZOOM Menu

equation

(

GRAPH

WIND

ZOOM

TRACE SOLVE

BOX

ZIN

ZOUT

ZFACT

ZSTD

BOX

Draws a box to redefine the viewing window (Chapter 6)

ZIN

Magnifies the graph around the cursor by factors of

xFact

and

yFact

(Chapter 6)

ZOUT

Displays more of the graph around the cursor by factors of

xFact

and

yFact

(Chapter 6)

ZFACT

Displays the

ZOOM

FACTORS

screen (Chapter 6)

ZSTD

Displays the graph in standard dimensions; resets the default window variable values
for

Func

graphing mode

The Simultaneous Equation Solver

The

imultaneous equation solver solves systems of up to 30 linear equations with 30 unknowns.

Entering Equations to Solve Simultaneously

��

Display the

SIMULT

number screen.

��

Enter an integer

‚

2 and

30 for the

number of equations. The coefficients-
entry editor for the first equation (for a
system of

equations and

unknowns) is

displayed. The

SIMULT ENTRY

menu also

is displayed.

Chapter 6 and the A to Z
Reference describe these
features in detail.

The

SIMULT

coefficients are

not variables.

You can display other menus
in the coefficients-entry
screen.

Summary of Contents for -86 - ViewScreen Calculator

Page 1: ...y CBL CBL 2 Calculator Based Ranger CBR Constant Memory Automatic Power Down APD and EOS are trademarks of Texas Instruments Incorporated Windows is a registered trademark of Microsoft Corporation IBM...

Page 2: ...e of these materials by any other party US FCC Information Concerning Radio Frequency Interference This equipment has been tested and found to comply with the limits for a Class B digital device pursu...

Page 3: ...Root 7 Calculating Derivatives 7 Retrieving Editing and Re evaluating the Previous Entry 8 Converting Degrees Fahrenheit to Degrees Celsius 8 Storing an Unevaluated Expression to an Equation Variable...

Page 4: ...he Last Entry 28 Retrieving and Editing the Last Entry 28 Retrieving Previous Entries 28 Retrieving Multiple Entries 29 Clearing the ENTRY Storage Area 29 Retrieving the Last Answer 29 Using Ans Prece...

Page 5: ...ants Conversions Bases and Complex Numbers 57 Using Built In and User Created Constants 58 The CONS Constants Menu 58 The CONS BLTIN Built In Constants Menu 58 Creating or Redefining a User Created Co...

Page 6: ...the Graph Style in the Equation Editor 80 Using Shading Patterns to Differentiate Functions 80 Viewing and Changing On Off Status of Stat Plots 81 Setting the Window Variables 81 Displaying the Window...

Page 7: ...8 Turning On or Turning Off Points 108 Chapter 7 Tables 109 Displaying the Table 110 TABLE Menu 110 The Table 110 Independent and Dependent Variables in the Table 111 Navigating the Table 111 The Tabl...

Page 8: ...ic Graph 130 Chapter 10 Differential Equation Graphing 131 Defining a Differential Equation Graph 132 Setting Differential Equation Graphing Mode 132 The GRAPH Menu 133 Setting the Graph Format 133 Di...

Page 9: ...ng Mathematical Functions with Lists 161 Attaching a Formula to a List Name 162 Comparing an Attached List with a Regular List 163 Using the List Editor to Attach a Formula 163 Using the List Editor W...

Page 10: ...Statistical Data 189 The LIST NAMES Menu 189 The STAT CALC Calculations Menu 189 Automatic Regression Equation Storage 191 Results of a Statistical Analysis 192 The STAT VARS Statistical Variables Me...

Page 11: ...ther Program Name 225 Using and Deleting Variables within a Single Program 225 Running an Assembly Language Program 225 Entering and Storing a String 226 The STRNG String Menu 227 Creating a String 22...

Page 12: ...ulus 246 Electrical Circuits 248 Program Taylor Series 250 Characteristic Polynomial and Eigenvalues 252 Convergence of the Power Series 254 Reservoir Problem 256 Predator Prey Model 258 Program Sierp...

Page 13: ...h Bob Fedorisko Revised 02 13 01 1 51 PM Printed 02 13 01 2 59 PM Page 1 of 14 Preparing to Use Your New TI 86 2 Calculating on the Home Screen 3 Plotting Functions on the Graph Screen 9 F1 F2 F3 F4 F...

Page 14: ...ompartment Turning On and Turning Off the TI 86 To turn on the TI 86 press which is in the bottom left corner of the keyboard You should see the entry cursor blinking in the top left corner of the scr...

Page 15: ...and integer part examples Otherwise the screens your TI 86 shows may differ from the screens pictured next to the activities Calculating the Sine of a Number Enter the sine function Enter a value You...

Page 16: ...en square it 1 V I Evaluate The value stored to the variable V is squared and displayed b Editing an Expression Enter the expression 25 14 4N3 2 D 25 14 E D 4 T 3 2 E Change 3 2 to 2 3 2 3 Move the cu...

Page 17: ...ss to display more Using a List with a Function Enter the exponential function Display the LIST menu and then select the open brace from the LIST menu On the TI 86 specifies the beginning of a list LI...

Page 18: ...MATH NUM menu Select the iPart integer part function from the MATH NUM menu iPart is pasted to the screen The previous entry was left on the screen to illustrate the effect of iPart on the previous a...

Page 19: ...age 7 of 14 Finding the Square Root Paste the square root function to the screen Enter a value for which you want to find the square root 144 Evaluate the expression The square root of 144 is displaye...

Page 20: ...NV menu shifts up and TEMP is highlighted Enter the known measurement If the measurement is negative use parentheses In this example if you omit parentheses the TI 86 converts 4 F to about L15 5 C whi...

Page 21: ...ph the functions y1 5 sin x and y2 5 cos x Plotting Functions on the Graph Screen The TI 86 plots four types of functions on the graph screen To plot a graph you must store an unevaluated expression t...

Page 22: ...is highlighted This indicates that both equations are selected to be graphed Chapter 5 5 D 2 E Changing the Graph Style of a Function In the equation editor the icon to the left of each equation speci...

Page 23: ...lotted in the order in which it is listed in the equation editor i free moving cursor When the graph is plotted you can move the free moving cursor around the graph screen The cursor coordinates are d...

Page 24: ...e Enter a real number or an expression that resolves to a real number that is within the dimensions of the current graph screen When you enter the first character the x prompt is displayed 6 Evaluate...

Page 25: ...screen Since xMin 0 only the first and fourth quadrants of the graph plane are displayed Deselecting a Function Select y x from the GRAPH menu to display the equation editor and equation editor menu...

Page 26: ...H ZOOM menu to activate the zoom box cursor Move the zoom box cursor to a point that is to be a corner of the redefined graph screen and then mark the point with a small square b Move the cursor away...

Page 27: ...g On and Turning Off the TI 86 17 Adjusting the Display Contrast 17 The Home Screen 18 Entering Numbers 19 Entering Other Characters 20 Entering Expressions and Instructions 24 Diagnosing an Error 27...

Page 28: ...bottom of the battery compartment and then push the cover until the latch snaps closed When to Replace Batteries When the AAA batteries are low a low battery message is displayed as you turn on the ca...

Page 29: ...s last displayed If Automatic Power DownTM APDTM previously had turned off the calculator the TI 86 will return as you left it including the display cursor and any error ON 1 0 2 3 6 5 4 ST S U Y Z V...

Page 30: ...e Screen When you first turn on your TI 86 the home screen is displayed Initially the home screen is a blank screen except for the entry cursor in the top left corner If you do not see the cursor pres...

Page 31: ...le when you press a plus sign is pasted to the cursor location This guidebook describes number entry keystrokes as 1 2 3 and so on instead of Y Z Entering Negative Numbers To enter a negative number p...

Page 32: ...b When you include scientific or engineering notation numbers in an expression the TI 86 does not necessarily display answers in scientific or engineering notation The mode settings page 34 and the si...

Page 33: ...is pasted to the cursor location X STAT 1 X returns an X When you press n the cursor becomes the lowercase alpha cursor When you press the next key the lowercase version of the blue character is past...

Page 34: ...sert __ Inserts a character at the cursor location and shifts remaining characters right Second Enters a 2nd character or executes a 2nd operation yellow on the keyboard ALPHA Enters an uppercase ALPH...

Page 35: ...tens screen contrast moves cursor right moves cursor to end of entry scrolls moves cursor up darkens screen contrast If you hold down or the cursor continues to move Inserting Deleting and Clearing Ch...

Page 36: ...r2 5 tan xStat and 40 L5 3 N 2 3 are expressions You can use an expression on the home screen to calculate an answer In most places where a value is required you can use an expression to enter the val...

Page 37: ...An instruction initiates an action For example ClDrw is an instruction that when executed clears all drawn elements from a graph You cannot use an instruction in an expression Generally the first lett...

Page 38: ...ly separate each from the next with a colon When you press b the TI 86 executes each entry from left to right and displays the result of the last expression or instruction The entire group entry is st...

Page 39: ...e such as ERROR 04 DOMAIN or ERROR 07 SYNTAX The Appendix describes each error type and possible reasons for the error If you select QUIT or press l or the home screen is displayed If you select GOTO...

Page 40: ...a storage area called ENTRY last entry When you turn off the TI 86 ENTRY is retained in memory To retrieve the last entry press The current line is cleared and the entry is pasted to the line Retrievi...

Page 41: ...s Store 8 to r as your first guess then execute pr2 8 X n R R 1 1 I b Retrieve 8 r pr2 and insert 7 958 as a new guess Continue guessing to approach the answer of 200 7 p 958 b Clearing the ENTRY Stor...

Page 42: ...area of a garden plot 1 7 meters by 4 2 meters Calculate the yield per square meter if the plot produces a total of 147 tomatoes 1 7 M 4 2 b 147 F b Using Ans Preceding a Function Previous answers are...

Page 43: ...displays the MATH menu Select a menu name from another menu displays the MATH NUM menu Select an editor or selection screen displays the list editor menu with the list editor Accidentally commit an e...

Page 44: ...layed To select a menu item press the menu selection key directly below the item For example in the MATH menu to the right press to select NUM press to select PROB and so on When you select a menu ite...

Page 45: ...and you select an item from the lower menu that displays yet another menu the editor menu remains as the upper menu When you select NUM from the lower menu The MATH menu disappears the equation editor...

Page 46: ...decimal places Execute the change b Notation Modes Normal Displays results with digits to the left and right of the decimal as in 123456 7 Sci scientific Displays results in two parts significant digi...

Page 47: ...degrees Complex Number Modes RectC rectangular complex mode Displays complex number results as real imaginary PolarC polar complex mode Displays complex number results as magnitude angle Graphing Mod...

Page 48: ...or three element vectors SphereV spherical vector coordinates Displays results in the form r q for two element vectors and r q f for three element vectors Differentiation Modes dxDer1 exact differenti...

Page 49: ...02 13 01 2 18 PM Printed 02 13 01 3 00 PM Page 37 of 10 The CATALOG 38 Storing Data to Variables 39 Classifying Variables as Data Types 42 The CUSTOM Menu 44 The CHAR Character Menu 45 F1 F2 F3 F4 F5...

Page 50: ...e item and press b The CATALOG disappears and the name is pasted to the previous cursor location Use or to move 4 to an item and press b The item is pasted to the cursor location To jump Do this To th...

Page 51: ...ore values to some of them They are introduced in the appropriate chapters of this guidebook Creating a Variable Name You can create your own variable name when you use X or a Name prompt to store dat...

Page 52: ...le is displayed as a result b Storing an Unevaluated Expression When you store an expression to memory using X with the sign the expression is evaluated and the result is stored to a variable When you...

Page 53: ...to variableB the syntax is variableA variableB For example RegEq y1 stores the regression equation Chapter 14 to the variable y1 Displaying a Variable Value With the cursor on a blank line on the home...

Page 54: ...cursor returns b Classifying Variables as Data Types The TI 86 classifies variables according to data type and places each variable on a data type selection screen You can display each screen by sele...

Page 55: ...complex number variables LIST Displays a selection screen with all list names VECTR Displays a selection screen with all vector names MATRX Displays a selection screen with all matrix names STRNG Disp...

Page 56: ...ens program names functions instructions and other items to create your own CUSTOM menu To display your CUSTOM menu press 9 Use through and to select items like any other menu Entering CUSTOM Menu Ite...

Page 57: ...a program to delete from memory one user created variable name except a program name and its contents the syntax is DelVar variable To delete user created variable names and their contents including p...

Page 58: ...SC GREEK INTL You can combine modifiers on the CHAR INTL menu with uppercase or lowercase vowels to create vowels used in some languages You can use these vowels in variable names and text Adding a Mo...

Page 59: ...sko Revised 02 13 01 2 19 PM Printed 02 13 01 3 00 PM Page 47 of 10 Keyboard Mathematical Functions 48 The MATH Menu 49 The CALC Calculus Menu 54 The TEST Relational Menu 55 F1 F2 F3 F4 F5 M1 M2 M3 M4...

Page 60: ...esults calculated on an element by element basis If you use two lists vectors or matrices in the same expression they must be equal in dimension Key Function Key Function add sin sine T N subtract cos...

Page 61: ...o 12 decimal places or to ofDecimals iPart value Returns the integer part or parts of value fPart value Returns the fractional part or parts of value int value Returns the largest integer less than or...

Page 62: ...a time rand Returns a random number 0 and 1 to control a random number sequence first store an integer seed value to rand such as 0 rand randInt lower upper ofTrials random integer Returns a random i...

Page 63: ...ven though you use degrees minutes seconds to enter a DMS angle The MATH HYP Hyperbolic Menu NUM PROB ANGLE HYP MISC sinh cosh tanh sinh 1 cosh 1 4 tanh 1 sinh value Returns the hyperbolic sine of val...

Page 64: ...urns a list in which each element is the value of expression evaluated for variable from begin to end by step lcm valueA valueB Returns the least common multiple of valueA and valueB gcd valueA valueB...

Page 65: ...x1 y1 The values can be expressions 3 b 5 b Enter values for the second known pair x2 y2 4 b 4 b Enter a value for either the x value or the y value of the unknown pair If necessary move the cursor t...

Page 66: ...Returns the value of the first derivative of expression with respect to variable for the current variable value or specified variable value der2 expression variable value Returns the value of the seco...

Page 67: ...pression evalF der1 der2 fMin fMax nDer seq and any equation variable such as y1 You can approximate the fourth derivative at the current value of x with this formula nDer nDer der2 x 4 x x x The TEST...

Page 68: ...ual to valueB valueA and valueB must be real numbers or lists valueA valueB not equal to Returns 1 if valueA is not equal to valueB returns 0 if valueA is equal to valueB valueA and valueB can be real...

Page 69: ...2 13 01 2 20 PM Printed 02 13 01 3 01 PM Page 57 of 16 Using Built In and User Created Constants 58 Converting Units of Measure 61 Number Bases 65 Using Complex Numbers 70 F1 F2 F3 F4 F5 M1 M2 M3 M4 M...

Page 70: ...tored to it The CONS BLTIN menu items are common constants built into the TI 86 You cannot edit the value of a built in constant You can create your own constants and add them to the user created cons...

Page 71: ...m2 C2 ec Electron charge 1 60217733EL19 C Rc Gas constant 8 31451 J mole K Gc Gravitational constant 6 67259EL11 N m2 kg2 g Earth acceleration due to gravity 9 80665 m sec2 Me Mass of an electron 9 1...

Page 72: ...prompt and the CONS EDIT menu is displayed see below A n U b Enter the real or complex constant value which can be an expression The value is stored to the constant as you enter it The user created co...

Page 73: ...n one unit into its equivalent value in another unit of measure For example you can convert inches to yards quarts to liters or degrees Fahrenheit to degrees Celsius The units of measure from which an...

Page 74: ...F from the conversion group menu The unit abbreviation is pasted to the cursor location Convert the measurement b The CONV Conversions Menu LNGTH AREA VOL TIME TEMP 4 MASS FORCE PRESS ENRGY POWER 4 S...

Page 75: ...lt yr light years fath fathoms The CONV AREA Menu ft2 square feet km2 square kilometers cm2 square centimeters m2 square meters acre acres yd2 square yards mi2 square miles in2 square inches ha hecta...

Page 76: ...FORCE Menu N Newtons tonf ton force lbf pound force dyne dynes kgf kilogram force The CONV PRESS Pressure Menu atm atmospheres lb in2 pounds per square inch inHg inches of mercury bar bars mmHg milli...

Page 77: ...s 131 km hr rounded up You also can return this result using only a forward slash as in 325mile4km 4hr4hr Number Bases The number base mode setting Chapter 1 controls how the TI 86 interprets an enter...

Page 78: ...al Equivalent Binary 1000 0000 0000 0001b 0111 1111 1111 1111b L32 767 32 767 Octal 5120 6357 4134 0001o 2657 1420 3643 7777o L99 999 999 999 999 99 999 999 999 999 Hexadecimal 50 85 001h 0000 5 3 107...

Page 79: ...e the number keys as you would for a decimal number Select the hexadecimal characters through from the menu as needed The BASE TYPE Menu TYPE CONV BOOL BIT In an expression you can designate a number...

Page 80: ...ct Displays value as octal value4Hex Displays value as hexadecimal value4Dec Displays value as decimal Converting Number Bases In Dec mode solve 10 10 10 10 10 10 b 35 Add 1 to the result and convert...

Page 81: ...nts are compared as this table shows Results If valueA is and valueB is and or xor not valueA 1 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 1 1 0 0 0 0 0 1 The result is displayed according to the current mode sett...

Page 82: ...component real imaginary magnitude or angle can be a real number or an expression that evaluates to a real number expressions are evaluated when you press b When RectC complex number mode is set compl...

Page 83: ...ngle 4 4Rec 4Pol conj real imaginary Returns the complex conjugate of a complex value list vector or matrix the result is real Limaginary conj magnitude angle Returns magnitude Langle real real imagin...

Page 84: ...command and only when complexValue is indeed complex complexValue 4Pol Displays complexValue in polar format magnitude angle regardless of complex mode setting valid only at the end of a command and o...

Page 85: ...M Printed 02 13 01 3 01 PM Page 73 of 14 Defining a Graph 74 Setting the Graph Mode 74 The GRAPH Menu 75 Using the Equation Editor 76 Setting the Window Variables 81 Setting the Graph Format 83 Displa...

Page 86: ...odes Set the graphing mode page 74 Define edit or select one or more functions in the equation editor pages 76 and 77 Select the graph style for each function page 79 Deselect stat plots if necessary...

Page 87: ...Der1 or dxNDer differentiation mode affects plotting of selected functions The GRAPH Menu 6 y x WIND ZOOM TRACE GRAPH 4 MATH DRAW FORMT STGDB RCGDB 4 EVAL STPIC RCPIC y x Displays the equation editor...

Page 88: ...d STPIC menu use this prompt to enter a PIC variable RCPIC Displays the Name prompt and RCPIC menu use this menu to recall a picture Using the Equation Editor To display the equation editor in Func gr...

Page 89: ...functions in the equation editor ALLN Deselects all defined functions in the equation editor STYLE Assigns the next of seven available graph styles to the function that the cursor is on Defining a Fun...

Page 90: ...nd then enter the appropriate number To insert the contents of an equation variable use RCL Chapter 1 To enter the equation variable at the Rcl prompt use the ALPHA keys alpha keys and other character...

Page 91: ...on a Ferris wheel using Icon Style Characteristics of the Plotted Function Line A solid line connects each plotted point this is the default in Connected mode Thick A thick solid line connects each p...

Page 92: ...ph only Using Shading Patterns to Differentiate Functions When you select shade above or shade below for more than one function the TI 86 rotates through a series of four shading patterns First shaded...

Page 93: ...on the graph screen By setting window variables you can define the graph screen window boundaries and other attributes xMin xMax yMin and yMax are the graph screen boundaries xScl x scale is the numbe...

Page 94: ...x resolution is below yScl on the window editor Changing a Window Variable Value Display the window editor Move the cursor to the window variable you want to change Edit the value which can be an exp...

Page 95: ...he steps above for changing a window variable value from the home screen or in the program editor When you change the values stored to x and y the TI 86 automatically recalculates xMax and yMax from x...

Page 96: ...ws a line between the points calculated for the functions in the equation editor DrawDot Plots only the calculated points for the functions in the equation editor SeqG sequential graphing Evaluates an...

Page 97: ...ogram Chapter 16 To use graphing commands on the home screen select them from the CATALOG or entering the individual characters Pausing or Stopping a Graph in Progress To pause graph plotting press b...

Page 98: ...on 2 4 6 sin 1 2 3 x also graphs three functions 2 sin x 4 sin 2x and 6 sin 3x Smart Graph Smart Graph displays the previously displayed graph when you press 6 as long as all factors that would cause...

Page 99: ...02 13 01 3 01 PM Page 87 of 22 Graph Tools on the TI 86 88 Tracing a Graph 90 Resizing the Graph Screen with ZOOM Operations 91 Using Interactive Math Functions 95 Evaluating a Function for a Specifi...

Page 100: ...E GRAPH 4 MATH DRAW FORMT STGDB RCGDB 4 EVAL STPIC RCPIC ZOOM Displays the GRAPH ZOOM menu use these items to apply preset graph screen dimensions TRACE Activates the trace cursor use this cursor to t...

Page 101: ...On format the x and y cursor coordinates are displayed at the bottom of the graph screen as you move the cursor Graphing Accuracy The coordinate values displayed as you move the cursor approximate act...

Page 102: ...on the current equation value b From one function to another function at x in the order or reverse order of the selected functions in the equation editor or From one member to another member of a fami...

Page 103: ...ing cursor press or 6 To resume tracing select TRACE from the GRAPH menu If Smart Graph has not replotted the graph Chapter 5 the trace cursor is at the point where you stopped tracing Resizing the Gr...

Page 104: ...comes the midpoint of the new graph ZTRIG Sets built in window variables appropriate for trigonometric functions in Radian mode xMin L8 24668071567 xScl 1 5707963267949 p 2 yMax 4 xMax 8 24668071567 y...

Page 105: ...Factors Zoom factors define the magnification or reduction factor by which ZIN ZOUT ZOOMX and ZOOMY zoom in or zoom out around a point To display the zoom factors editor select ZFACT from the GRAPH Z...

Page 106: ...the current graph unless you press a key other than b or To zoom in or zoom out again at the same point press b To zoom in or zoom out at a new center point move the cursor and press b To zoom out on...

Page 107: ...graphing mode only zqMin zqMax and zqStep Param graphing mode only ztMin ztMax and ztStep DifEq graphing mode only ztMin ztMax ztStep and ztPlot Using Interactive Math Functions When you select a GRAP...

Page 108: ...function s y intercept y at x 0 ISECT Finds the intersection of two functions using a specified left bound right bound and guess DIST Finds the straight line distance between a specified left bound an...

Page 109: ...the left bound for x Either move the trace cursor to the left bound or enter a value directly Right Bound is displayed a 3 b or b Specify the right bound for x as in step 3 Guess is displayed Guess a...

Page 110: ...alue Right Bound is displayed b or value b DIST only If you want the right bound to be a point on another function move the cursor to the other function Select the right bound Either move the cursor t...

Page 111: ...rom the GRAPH MATH menu The current graph is displayed Move the cursor to the function with the point for which you want to find the derivative or slope 6 Move the cursor to the point or enter the x v...

Page 112: ...e next function and Second Curve is displayed 6 b Select the second function curve Guess is displayed Guess the intersection Either move the cursor to a point near an intersection or enter an x value...

Page 113: ...coordinate values are displayed The number in the top right corner indicates which function is evaluated b Move the result cursor to the next or previous selected function The result cursor is on the...

Page 114: ...ents that define the current graph to a graph database GDB variable select STGDB from the GRAPH menu These information types are stored to a GDB variable Equation editor functions Window variable valu...

Page 115: ...PTOFF PTCHG 4 CLDRW PxOn PxOff PxChg PxTest 4 TEXT TanLn DrInv You can use these GRAPH DRAW menu items only on the home screen or in the program editor Shade Shades a specified area of a graph See pag...

Page 116: ...lt 2 every second pixel 3 every third pixel 4 every fourth pixel 5 every fifth pixel 6 every sixth pixel 7 every seventh pixel 8 every eighth pixel The area that is specifically above lowerFunc and be...

Page 117: ...the point at the cursor location PTOFF Turns off the point at the cursor location PTCHG Changes the on off status of a point at the cursor location CLDRW Clears all drawings from the graph screen repl...

Page 118: ...repeat steps 2 and 3 to cancel VERT or HORIZ press Drawing a Circle Select CIRCL from the GRAPH DRAW menu The graph is displayed Define the center point of the circle with the cursor 6 b Move the cur...

Page 119: ...d its y values on the x axis DrInv is available only in Func graphing mode DrawF expression TanLn expression x DrInv expression DrawF x 3 3x2 4x TanLn y1 1 5 DrInv y1 Drawing Freehand Points Lines and...

Page 120: ...top right corner Move the cursor to another location Enter max alpha lock remains on n 1 M I N M A X Turning On or Turning Off Points Select PTON or PTOFF from the GRAPH DRAW menu Move the cursor to w...

Page 121: ...86 Chap 7 US English Bob Fedorisko Revised 02 13 01 2 25 PM Printed 02 13 01 3 02 PM Page 109 of 6 Displaying the Table 110 Setting Up the Table 113 Clearing the Table 114 F1 F2 F3 F4 F5 M1 M2 M3 M4 M...

Page 122: ...in the table represents a selected function stored in the equation editor for the current graphing mode TABLE Menu 7 TABLE TBLST table screen table setup editor The Table 7 independent variable value...

Page 123: ...on t Q1 through Q9 Navigating the Table To Do this Display more dependent variables in the table Press or Display greater values in any column Press only when Indpnt Auto is set page 112 Set TblStart...

Page 124: ...s the table setup editor SELCT On the edit line deselects or cancels deselection of the equation x and y q and r t xt and yt or t and Q On the edit line pastes the variable to the cursor location the...

Page 125: ...Tbl is positive then the values of x q or t increase as you scroll down the table If Tbl is negative then the values of x q or t decrease as you scroll down the table Indpnt Auto displays independent...

Page 126: ...olumn until the name is highlighted 7 Display the equation in the edit line b Edit the equation Enter the edited equation The dependent variable values are recalculated 5 1 b The cursor returns to the...

Page 127: ...sh Bob Fedorisko Revised 02 13 01 2 26 PM Printed 02 13 01 3 02 PM Page 115 of 8 Preview Polar Graphing 116 Defining a Polar Graph 117 Using Graph Tools in Pol Graphing Mode 119 F1 F2 F3 F4 F5 M1 M2 M...

Page 128: ...for A 8 and B 2 5 Then explore the appearance of the flower for other values of A and B Select Pol mode from the mode screen m b Display the equation editor and polar equation editor menu Deselect or...

Page 129: ...ols Chapter 8 details aspects of polar graphing that differ from function graphing Setting Polar Graphing Mode To display the mode screen press m To graph polar equations you must select Pol graphing...

Page 130: ...ficient memory is available Equations are defined in terms of the independent variable q The default graph style is line in Pol graphing mode shade above and shade below graph styles are not available...

Page 131: ...q the variables that define the equations Displaying the Graph To plot the selected polar equations you can select GRAPH TRACE EVAL RCGDB or a ZOOM MATH DRAW or RCPIC operation from the GRAPH menu The...

Page 132: ...Min In RectGC format moving the trace cursor updates the values of q x and y if CoordOn format is selected q x and y are displayed In PolarGC format moving the trace cursor updates x y r and q if Coor...

Page 133: ...lue you enter must be valid for the current graph screen When you have completed the entry press b to reactivate the trace cursor Using Zoom Operations The GRAPH ZOOM menu items except ZFIT work the s...

Page 134: ...rectangular coordinate plane dy dx and dr dq are independent of the RectGC or PolarGC format At a point where the derivative is undefined TANLN will draw the line but no result is displayed or stored...

Page 135: ...edorisko Revised 02 13 01 2 27 PM Printed 02 13 01 3 02 PM Page 123 of 8 Preview Parametric Graphing 124 Defining a Parametric Graph 125 Using Graph Tools in Param Graphing Mode 128 F1 F2 F3 F4 F5 M1...

Page 136: ...does it go Select Param mode from the mode screen m b Display the equation editor and parametric equation editor menu Deselect all equations and plots if any are defined Define the path of the ball a...

Page 137: ...raph screen b b Plot the graph The plotting action simultaneously shows the ball in flight and the vertical and horizontal component vectors of the motion Trace the graph to obtain numerical results T...

Page 138: ...Equation Editor To display the parametric equation editor select E t from the GRAPH menu in Param graphing mode 6 The equation editor menu displayed on the bottom line is the same as the Func mode eq...

Page 139: ...xt or yt and then select DELf from the equation editor menu Both components are deleted To delete a parametric equation using the MEM DELET menu Chapter 17 you must select the xt component If you sel...

Page 140: ...Min to tMax in intervals of tStep and then plots each point defined by x and y As the graph is plotted the variables x y and t are updated Using Graph Tools in Param Graphing Mode The Free Moving Curs...

Page 141: ...tely If you have graphed a family of curves and move through each curve before moving to the next parametric function Moving the Trace Cursor to a t Value To move the trace cursor to any valid t value...

Page 142: ...point with respect to t dx dt Returns the derivative of the xt equation at a point with respect to t The distances calculated by DIST and ARC are distances in the rectangular coordinate plane At a poi...

Page 143: ...2 13 01 2 28 PM Printed 02 13 01 3 02 PM Page 131 of 20 Defining a Differential Equation Graph 132 Entering and Solving Differential Equations 139 Using Graph Tools in DifEq Graphing Mode 144 F1 F2 F3...

Page 144: ...modes in these ways You must select the field format or accept the default before defining the equations page 133 If an equation is higher than first order you must convert it to an equivalent system...

Page 145: ...t To display the format screen in DifEq graphing mode select FORMT from the GRAPH menu 6 The RK Euler and SlpFld DirFld FldOff format settings are available only in DifEq mode The RectGC PolarGC DrawL...

Page 146: ...the y axis FldOff field off Graphs all selected differential equations with t or Q1 on the x axis Q1 or Q2 on the y axis and no field initial conditions must be defined for all equations page 136 The...

Page 147: ...quation system it references all equations in the equation editor regardless of selection status starting at Q 1 You must define Q n equation variables consecutively starting at Q 1 For example if Q 1...

Page 148: ...at which plotting begins ignored when t is an axis difTol 001 in RK format Specifies tolerance to help select step size for solving must be 1EL12 EStep 1 in Euler format Specifies Euler iterations be...

Page 149: ...ne axis and Qn or Q n to the other axis only the equation stored to Qn or Q n is plotted other differential equations in the equation editor are not plotted their selection status is ignored dTime is...

Page 150: ...ing a graph style These actions update fldPic Editing an equation in the equation editor Re assigning an axis editing a dTime value or editing a fldRes value Using a GRAPH ZOOM menu item Changing a fo...

Page 151: ...nt variable and Q n is the equation variable in DifEq graphing mode Therefore when you enter an equation in the differential equation editor you must express it in terms of t and Q n For example to ex...

Page 152: ...aph are not very illustrative i Change the window variables xMin xMax yMin and yMax Select TRACE from the GRAPH menu to re plot the graph and activate the trace cursor Trace the solution The trace cur...

Page 153: ...or substituting Q1 for y and Q2 for y 2 a 1 Display the initial conditions editor and enter the initial conditions if you want a specific solution To enter a list of initial conditions use and from th...

Page 154: ...equation y 4 Ny eLx into an equivalent system of first order differential equations as shown in the chart below Differentiate Define the variables as And then substitute t x Q 1 y Q1 y Q 1 Q2 since Q...

Page 155: ...e 143 of 20 Display the window editor and set the window variable values f 10 01 0 a 4 4 Display the initial conditions editor and enter the initial conditions A small square indicates that an initial...

Page 156: ...r works in DifEq mode as it does in Func graphing The cursor coordinate values for x and y are displayed and the variables are updated Tracing a Differential Equation To begin a trace select TRACE fro...

Page 157: ...r the current graph screen When you have completed the entry press b to reactivate the trace cursor Drawing on a Differential Equation Graph The GRAPH DRAW menu items work the same in DifEq graphing m...

Page 158: ...ist yList or tList as a stat plot after you draw the equation and then trace them Chapter 14 Also you can fit statistical regression models to the lists Chapter 14 Display the mode screen and set DifE...

Page 159: ...he Again prompt is displayed and ALPHA lock is on for Y and N only To use DrEqu again with new initial conditions press Y or b To leave DrEqu and display the GRAPH menu press N or Using ZOOM Operation...

Page 160: ...orisko Revised 02 13 01 2 28 PM Printed 02 13 01 3 02 PM Page 148 of 20 Drawing Solutions Interactively with EXPLR Display the mode screen and set DifEq graphing mode m b Display the format screen and...

Page 161: ...cursor to the initial condition for which you want to solve Draw the solution to Q1 using the cursor coordinates x y as initial condition t Q 1 t b To continue drawing more solutions move the free mo...

Page 162: ...10 US English Bob Fedorisko Revised 02 13 01 2 28 PM Printed 02 13 01 3 02 PM Page 150 of 20 Evaluating Differential Equations for a Specified t When the trace cursor is not active the GRAPH menu ite...

Page 163: ...rinted 02 13 01 3 03 PM Page 151 of 16 Lists on the TI 86 152 Creating Storing and Displaying Lists 153 The List Editor 156 Using List Operations 159 Using Mathematical Functions with Lists 161 Attach...

Page 164: ...the Calculator Based Laboratory CBL 2 CBL or Calculator Based Ranger CBR and store it to a list name on the TI 86 Chapter 18 Create lists dynamically using the LIST OPS menu item seq page 159 On the T...

Page 165: ...Entering a List Directly in an Expression To enter a list directly the syntax is element1 element2 element n Enter any part of the expression that precedes the list Select from the LIST menu to begin...

Page 166: ...the example begin these steps at step 2 Paste to the cursor location ALPHA lock is on steps 2 through 5 above X Enter the list name Either select a name from the LIST NAMES menu or directly enter a na...

Page 167: ...ay the list element D 4 E b Storing a New Value to a List Element To store a value to a current element or one element beyond the end of a list the syntax is value listName element Enter the value to...

Page 168: ...list names and attach formulas to lists in the list editor List names Table of elements Entry line with current column list name and element number Current column number List editor menu The List Edit...

Page 169: ...Name into the List Editor Move the cursor to column 3 Insert a new unnamed column List names shift right clearing column 3 The Name prompt and LIST NAMES menu are displayed p Select ABC12 from the LIS...

Page 170: ...ny expression is evaluated and the value is stored to the current element b or or Deleting Elements from a List To delete a single element from a list move the cursor onto the element and press 3 The...

Page 171: ...sum prod seq li4vc vc4li 4 Fill aug cSum Deltal Sortx 4 Sorty Select SetLE Form dimL list Returns the dimension of or number of elements in list ofElements dimL listName Creates listName as a list th...

Page 172: ...ector vc4li vector vc4li element1 element2 Converts a real or complex vector to a list Fill number listName Stores a real or complex number to every element of listName aug listA listB augment Concate...

Page 173: ...and fStat to columns 1 2 and 3 Form formula listName Attaches formula to listName formula resolves to a list which is dynamically stored and updated in listName page 162 Using Mathematical Functions w...

Page 174: ...formula is attached are updated To attach a formula to a list name on the home screen or in the program editor the syntax is Form formula listName When you enter a new list name as the second argumen...

Page 175: ...xpression L1 10 to the list name LX 1 L 1 10 X L X b Change the second element in L1 to L8 and display the edited list a 8 X L 1 1 D 2 E 1 L 1 b Compare the elements of the regular list LX with ADD10...

Page 176: ...in the list to which the formula is attached When you edit or enter elements of a displayed list in any of the three current list editor columns while an attached formula list also is displayed the T...

Page 177: ...list editor using the LIST OPS menu item SetLE page 161 Handling Errors Related to Attached Formulas On the home screen you can attach to a list a formula that references another list that has no ele...

Page 178: ...ess b b All list elements remain but the formula is detached and the lock symbol disappears In the list editor move the cursor onto an element of the attached formula list Press b edit the element and...

Page 179: ...b Fedorisko Revised 02 13 01 2 31 PM Printed 02 13 01 3 03 PM Page 167 of 10 Vectors on the TI 86 168 Creating Storing and Displaying Vectors 169 Using Mathematical Functions with Vectors 176 F1 F2 F3...

Page 180: ...displayed horizontally When you use a vector in an expression the TI 86 automatically interprets the vector in the form row vector or column vector that is appropriate for the expression For example...

Page 181: ...current cursor location select it from the menu Creating a Vector in the Vector Editor Display the vector Name prompt screen ALPHA lock is on The VECTR NAMES menu is displayed Enter a name from one t...

Page 182: ...ent en prompt at the cursor location shifts current elements down DELi Deletes the element from the cursor location and from the vector shifts elements up 4REAL Converts the displayed complex number v...

Page 183: ...r complexVectorName realVector contains the real part of each element and imaginaryVector contains the imaginary part Displaying a Vector To display a vector paste the vector name to the home screen a...

Page 184: ...n select the vector name from the VARS VECTR screen w Editing Vector Dimension and Elements Display the vector Name prompt screen Enter the vector name Either select it from the VECTR NAMES menu or en...

Page 185: ...e Frobenius norm G real2 imaginary2 where the sum is over all elements of a real or complex vector dot vectorA vectorB Returns the dot product of vectorA and vectorB both of which are real or complex...

Page 186: ...he three element vector conversion equations for spherical form r q f are x r cosq sinf y r sinq sinf z r cosf vector4Pol Displays a 2 element vector in polar form r q vector4Cyl Displays a 2 or 3 ele...

Page 187: ...nt of a complexVector imag complexVector Returns a real vector in which each element is the imaginary portion of the corresponding element of a complexVector abs Vector Returns a real vector in which...

Page 188: ...mension and vector dimension must be equal vector number Returns a vector that is the quotient of each real or complex vector element divided by a real or complex number Mvector negation Changes the s...

Page 189: ...Fedorisko Revised 02 13 01 2 32 PM Printed 02 13 01 3 03 PM Page 177 of 10 Matrices on the TI 86 178 Creating Storing and Displaying Matrices 178 Using Mathematical Functions with Matrices 185 F1 F2 F...

Page 190: ...e matrix name Creating Storing and Displaying Matrices The MATRX Matrix Menu NAMES EDIT MATH OPS CPLX matrix names matrix math complex matrix menu menu menu matrix matrix operations editor menu The MA...

Page 191: ...lement value at the element prompt 1 1 for row 1 column 1 You can enter expressions To move to the next element press b To move to the next row press a 4 b 5 b 9 b 6 b 1 b a 3 b 7 b and so on The Matr...

Page 192: ...ix with a 1 P a 3 P a 5 P a 7 Store the matrix to a matrix name Either enter a name from one to eight characters long starting with a letter or select a name from the MATRX NAMES menu The matrix is di...

Page 193: ...ts with very large values may be expressed exponentially To display specific elements of matrixName the syntax is matrixName row column To display a row of matrixName the syntax is matrixName row To d...

Page 194: ...ension b 5 3 b 3 b Move the cursor to any element and edit it Continue moving the cursor to other elements Save the changes and leave the matrix editor 45 b 21 b 2 b Editing Matrices on the Home Scree...

Page 195: ...areMatrix Returns a matrix containing the eigenvectors for a real or complex squareMatrix each column corresponds to an eigenvalue rnorm matrix row norm Returns the largest of the sums of the absolute...

Page 196: ...t dimension Returns the square identity matrix of dimension dimension ref matrix Returns the row echelon form of matrix rref matrix Returns the reduced row echelon form of matrix aug matrixA matrixB C...

Page 197: ...g element of a complexMatrix abs matrix Returns a real matrix in which each element is either the absolute value of the corresponding element of a real matrix or the magnitude modulus of the correspon...

Page 198: ...uareMatrix Returns the square matrix exponential of a real squareMatrix sin squareMatrix Returns the square matrix sine of a real squareMatrix cos squareMatrix Returns the square matrix cosine of a re...

Page 199: ...13 01 3 04 PM Page 187 of 14 Statistical Analysis on the TI 86 188 Setting Up a Statistical Analysis 188 Results of a Statistical Analysis 192 Plotting Statistical Data 194 The STAT DRAW Menu 199 Fore...

Page 200: ...le data has pairs comprising an independent variable and a dependent variable When analyzing either kind of data you can specify a frequency of occurrence for the independent variable values These spe...

Page 201: ...omatically updated list of the frequency values used in the last statistical computation requiring a frequency default is a list where each element is 1 xStat An automatically updated list of the data...

Page 202: ...ast four data points it also requires at least two data points per cycle to avoid aliased frequency estimates LgstR logistic regression Fits the model equation y a 1 becx d to the data displays a b c...

Page 203: ...the syntax is LgstR iterations xList yList frequencyList equationVariable To copy the contents RegEq to any variable after calculating the regression the syntax is StReg variable Automatic Regression...

Page 204: ...f you edit a list or change the type of analysis all statistical variables are cleared The STAT VARS Statistical Variables Menu CALC EDIT PLOT DRAW VARS v sx Sx w sy 4 Sy Gx Gx2 Gy Gy2 4 Gxy RegEq cor...

Page 205: ...Gx Gx max of x values maxX maxX sum of x2 values Gx2 Gx2 min of y values minY sum of y values Gy max of y values maxY sum of y2 values Gy2 median Med sum of x y Gxy 1st quartile Qrtl1 regression equat...

Page 206: ...e or more lists Chapter 11 Select or deselect functions in the current equation editor as appropriate Chapter 5 Define the statistical plot Turn on the plots you want to display Define the window vari...

Page 207: ...screen Press b All stat plots are now on or off Setting Up a Stat Plot To set up a stat plot select PLOT1 PLOT2 or PLOT3 from the STAT PLOT menu The stat plot editor for the selected stat plot is dis...

Page 208: ...u enter at the Xlist Name prompt is stored to the list name xStat Any list you enter at the Ylist Name prompt is stored to the list name yStat Any list you enter at the Freq prompt is stored to fStat...

Page 209: ...plot except that the points are 1 5 Interquartile Range beyond the quartiles The Interquartile Range is defined as the difference between the third quartile Q3 and the first quartile Q1 These points...

Page 210: ...yMax to include all values and also adjusts xScl xMax N xMin xScl 47 must be true A value that occurs on the edge of a bar is counted in the bar to the right For the example xStat 1 2 2 2 3 8 9 5 6 6...

Page 211: ...aws a modified box plot of the data points DRREG draw regression equation Draws the current regression equation CLDRW clear drawings Displays the current graph with no drawings DrawF expression draw f...

Page 212: ...regression for xStat and yStat The statistical results are displayed Remove the STAT CALC menu to display all results including n b Display the forecast editor The current regression model is display...

Page 213: ...Equation Solver 202 Entering an Equation in the Equation Entry Editor 203 Setting Up the Interactive Solver Editor 204 Solving for the Unknown Variable 206 Graphing the Solution 207 Solver Graph Tools...

Page 214: ...ottom of the screen Enter an equation When you press b the interactive solver editor and solver menu are displayed t 1 V 1 1 1 V D 1 R 1 F D 1 R 1 1 R 2 E E b Enter values for each variable except the...

Page 215: ...QU menu is a menu version of the VARS EQU screen Chapter 2 The items are all variables to which an equation is stored This includes all selected and deselected equation variables defined in the equati...

Page 216: ...the editor page 206 bound L1E99 1E99 is a list containing the default lower bound L1E99 and the default upper bound 1E99 You can edit the bounds below Entering Variable Values To solve for an unknown...

Page 217: ...und upperBound 2 as a guess On the solver graph page 207 you can guess a solution by moving the free moving cursor or trace cursor to a point on the graph between lowerBound and upperBound To solve fo...

Page 218: ...nknown Variable After you have stored all known variable values set the bounds and entered a guess optional move the cursor to the prompt for the unknown variable To solve select SOLVE from the solver...

Page 219: ...axis The solver graph Uses the current window and format settings Chapter 5 Does not graph the solution according to the current graphing mode Always graphs a solution as a function graph Does not gra...

Page 220: ...more of the graph around the cursor by factors of xFact and yFact Chapter 6 ZFACT Displays the ZOOM FACTORS screen Chapter 6 ZSTD Displays the graph in standard dimensions resets the default window va...

Page 221: ...ts entry screen for the second and third equation and enter values for them or b or 5 a 6 a 4 2 1 5 9 7 Solve the equations The results of the polynomial are calculated and displayed on the result scr...

Page 222: ...the results x1 x2 xn to a vector of dimension n select STOx To store a single value on the coefficients entry screen or result screen follow these steps Move the cursor to the sign next to the coeffic...

Page 223: ...displayed with the equation across the top the coefficient prompts along the left side and the POLY ENTRY menu on the bottom v 4 b Enter a real or complex value or an expression that resolves to one...

Page 224: ...he coefficient or root value you want to store Display the Sto prompt ALPHA lock is on Enter the variable to which you want to store the value Store the value X R O O T 1 1 b Display the Name prompt f...

Page 225: ...3 01 2 36 PM Printed 02 13 01 3 04 PM Page 213 of 16 Writing a Program on the TI 86 214 Running a Program 221 Working with Programs 223 Running an Assembly Language Program 225 Entering and Storing a...

Page 226: ...se most TI 86 features in a program Programs can retrieve and update all variables stored to memory Also the program editor menu has input output commands such as Input and Disp and program control co...

Page 227: ...y places a colon at the beginning of each command line As you write the program the commands are stored to the program name The Program Editor Menu 8 programName b PAGE PAGE I O CTL INSc 4 DELc UNDEL...

Page 228: ...le with to prompt you to enter a value for that variable Disp Displays the home screen Disp valueA valueB Displays each value Disp variableA variableB Displays the value stored to each variable Disp t...

Page 229: ...g Send is preferred on the TI 86 you can use Outpt to send listName to a CBL 2 CBL or CBR for TI 85 compatibility InpSt promptString variable InpSt variable Pauses a program displays promptString or a...

Page 230: ...ndition is true evaluates to a nonzero value the program continues on to the next command Then Following If executes a group of commands if condition is true Else Following If and Then executes a grou...

Page 231: ...th a letter Goto label Transfers control to the program branch labeled with label IS variable value Adds 1 to variable if the answer is value the next command is skipped if the answer is value the nex...

Page 232: ...acters may be abbreviated in the menu Entering a Command Line You can enter on a command line any instruction or expression that you could execute on the home screen In the program editor each new com...

Page 233: ...e home screen Either select it from the PRGM NAMES menu 8 or enter individual characters Press b The program begins to run Each result updates the last answer variable Ans Chapter 1 The TI 86 reports...

Page 234: ...nu Define the function assignment statement Clear the home screen PRGM I O menu Convert y1 into the string variable STRING STRNG menu Display y1 at row 1 column 1 PRGM I O menu Display value stored to...

Page 235: ...emory Chapter 17 Editing a Program After you write a program you can display it in the program editor and edit any command line Display the program editor 8 The PRGM NAMES menu also is displayed Enter...

Page 236: ...editor enter the subroutine program name on a command line by itself Press 8 to display the PRGM NAMES menu and then select the program name Use ALPHA keys and alpha keys to enter the program name s...

Page 237: ...to the other program at the cursor location Using and Deleting Variables within a Single Program If you want to use variables within a program but do not need them after the program is run you can use...

Page 238: ...from another program as a subroutine page 224 To run an assemblyProgramName the syntax is Asm assemblyProgramName If you write an assembly language program use the two instructions below from the CATA...

Page 239: ...ame Returns the number of characters in string or stringName Eq4St equationVariable stringName Converts equationVariable contents to stringName St4Eq stringName equationVariable Converts stringName to...

Page 240: ...2 13 01 2 36 PM Printed 02 13 01 3 04 PM Page 228 of 16 16PROG DOC TI 86 Chap 16 US English Bob Fedorisko Revised 02 13 01 2 36 PM Printed 02 13 01 3 04 PM Page 228 of 16 16PROG DOC TI 86 Chap 16 US E...

Page 241: ...English Bob Fedorisko Revised 02 13 01 2 37 PM Printed 02 13 01 3 05 PM Page 229 of 4 Checking Available Memory 230 Deleting Items from Memory 231 Resetting the TI 86 232 F1 F2 F3 F4 F5 M1 M2 M3 M4 M...

Page 242: ...Usage When all memory is cleared and all defaults are set the standard TI 86 has 98 224 bytes of available random access memory RAM As you store information to RAM you can monitor memory allocation o...

Page 243: ...e DELETE screens to delete any user created variable and the information stored to it Select DELET from the MEM menu to display the MEM DELET menu Select the data type of the item you want to delete T...

Page 244: ...are displayed MEM When confirmed clears all stored data from memory Mem Cleared is displayed DFLTS When confirmed resets all defaults Defaults Set is displayed When you select ALL MEM or DFLTS a conf...

Page 245: ...02 13 01 3 05 PM Page 233 of 10 TI 86 Linking Options 234 Connecting the TI 86 to Another Device 235 Selecting Data to Send 236 Preparing the Receiving Device 240 Transmitting Data 240 Receiving Trans...

Page 246: ...86 Linking a TI 86 and a TI 85 You can select the data types including programs to transfer from a TI 85 to a TI 86 You can send most variables and programs from a TI 86 to a TI 85 using SND85 page 23...

Page 247: ...NK and internet services you can download programs from TI s World Wide Web site at http www ti com calc You can download various programs from TI s web site including assembly language programs that...

Page 248: ...ng Data to Send To list the variables for a specific data type on a selection screen select the data type from the LINK SEND menu When you select BCKUP the message Memory Backup is displayed The LINK...

Page 249: ...writes all memory in the receiving unit all information in the memory of the receiving unit is lost To cancel initiation of a memory backup press As a safety check to prevent accidental loss of memory...

Page 250: ...select a specific variable to be sent use and to move the selection cursor next to the variable and then select SELCT from the selection screen menu To select all variables of this type select ALL fr...

Page 251: ...to send user created zoom window variables and format settings in any mode To complete transmission of the selected variables prepare the other unit to receive data transmission below and then select...

Page 252: ...ithout receiving items press When the LINK TRANSMISSION ERROR message is displayed select EXIT from the menu The LINK menu is displayed Transmitting Data After you select data types on the sending uni...

Page 253: ...iving calculator transmission is interrupted The duplicated variable name its data type and the DUPLICATE NAME menu are displayed as shown in the screen to the right To resume or cancel transmission y...

Page 254: ...it cable from the receiving unit connect it to another device prepare the device to receive data and then select SEND then ALL and then XMIT Error Conditions A transmission error occurs after a few se...

Page 255: ...ices 244 Finding the Area between Curves 245 The Fundamental Theorem of Calculus 246 Electrical Circuits 248 Program Taylor Series 250 Characteristic Polynomial and Eigenvalues 252 Convergence of the...

Page 256: ...A select aug from the MATRX OPS menu enter A select ident from the MATRX OPS menu and then enter 3 Execute the expression Enter Ans to which the matrix from step 3 is stored Define a submatrix that c...

Page 257: ...PH menu to display the graph screen Select ISECT from the GRAPH MATH menu Move the trace cursor to the intersection of the functions Press b to select y1 The cursor moves to y2 Press b Then press b ag...

Page 258: ...t t 0 x y3 nDer y2 x Select TOL from the MEM menu to display the tolerance editor To improve the rate of the calculations set tol 0 1 and d 0 001 Select WIND from the GRAPH menu and set the window va...

Page 259: ...TI 86 Chap 19 US English Bob Fedorisko Revised 02 13 01 2 41 PM Printed 02 13 01 3 05 PM Page 247 of 18 Deselect y2 in the equation editor Select TBLST from the TABLE menu Set TblStart 1 Tbl 1 and Ind...

Page 260: ...e editor and a regression forecast In two consecutive columns of the list editor store the current measurements shown below to the list name CURR and the voltage measurements shown below to the list n...

Page 261: ...s x1 POWER 7 y1 CURR 7 x2 POWER 8 y2 CURR 8 Enter y 125 and solve for x On the home screen select LinR from the STAT CALC menu to fit the linear regression model equation to the data stored to POWER a...

Page 262: ...enter this brief program to store the Mobius Series The program TAYLOR calls this program and runs it as a subroutine PROGRAM MOBIUS 1 L1 L1 0 L1 1 L1 0 0 1 L1 0 L1 1 1 0 L1 0 L1 0 MSERIES Return Sele...

Page 263: ...y13 x center 2 TPOLY orderN1 If order 3 Begins Then group Then Calls subroutine MOBIUS Begins For group For N 3 order 1 abs f0 gmax gmax bmi 1 m 0 ssum Begins While group While abs bmi H gmax While MS...

Page 264: ...and store them to the list name EV Graph the characteristic polynomial Cp x of matrix A without knowing the analytic form of Cp x based on the formula Cp x det ANx I In Func graphing mode select y x...

Page 265: ...ne seq is on the MATH MISC menu Create elements for yStat by attaching the formula y1 xStat to yStat in the entry line The expression is evaluated when you press b or exit the list editor On the home...

Page 266: ...hick graph style as shown y3 Lx 3 14xN24 Graph y1 y2 y3 and Plot1 Deselect y2 in the equation editor Select TABLE from the TABLE menu to display y1 and y3 in the table Compare the values for the chara...

Page 267: ...ation Select fnInt from the CALC menu xt2 t yt2 fnInt sin w w w 0 t Select WIND from the GRAPH menu and set the window variable values as shown tMin L15 xMin L15 yMin L3 tMax 15 xMax 15 yMax 3 tStep 0...

Page 268: ...he length of the water stream when the valve is wide open Assume a full tank at time 0 no acceleration in the x direction and no initial velocity in the y direction Also ignore valve size and valve ty...

Page 269: ...o xt2 For xt2 change the valve height which is 0 5 to 0 75 meters Do the same with yt1 and yt2 Repeat step 3 to create three more pairs of equations Change the valve height to 1 0 meters for xt3 and y...

Page 270: ...R 3RNF R Q1 population of foxes F Q2 population of rabbits R Q 1 initial population of foxes 2 Q 2 initial population of rabbits 5 Find the population of foxes and rabbits after 3 months t 3 In DifEq...

Page 271: ...GRAPH menu and delete the values for Q 1 and Q 2 Select GRAPH from the GRAPH menu to display the direction field of the phase plane solution To see a family of specific phase plane solutions on top of...

Page 272: ...RGM menu enter SIERP at the Name prompt and then enter this program PROGRAM SIERP FnOff ClDrw PlOff AxesOff Sets viewing window 0 xMin 1 xMax 0 yMin 1 yMax rand X rand Y Begins For group For K 1 3000...

Page 273: ...3 01 3 05 PM Page 261 of 118 20ATOZ DOC TI 86 Chap 20 US English Bob Fedorisko Revised 02 13 01 2 42 PM Printed 02 13 01 3 05 PM Page 261 of 118 Quick Find Locator 262 Alphabetical Listing of Operatio...

Page 274: ...Equ 287 DrInv 287 dxDer1 288 dxNDer 288 FldOff 295 FnOff 296 FnOn 297 Func 299 GridOff 301 GridOn 302 GrStl 302 Horiz 304 LabelOff 310 LabelOn 310 Line 314 Param 333 Pol 336 PolarGC 336 PtChg 338 PtOf...

Page 275: ...91 evalF 292 Exponent E 292 Factorial 294 Fix 295 Float 295 fMax 296 fMin 296 fnInt 296 fPart 298 4Frac 298 gcd 299 Greater than 300 Greater than or equal to 301 302 Hex 302 4Hex 303 imag 306 int 308...

Page 276: ...3 DelVar 280 Disp 283 DispG 283 DispT 284 DS 288 Else 290 End 290 Equal 290 Equal to 291 For 297 Get 299 getKy 300 Goto 300 IAsk 304 IAuto 304 If 305 InpSt 307 Input 307 IS 310 Lbl 311 LCust 311 Menu...

Page 277: ...20ATOZ DOC TI 86 Chap 20 US English Bob Fedorisko Revised 02 13 01 2 42 PM Printed 02 13 01 3 05 PM Page 265 of 118 Strings Concatenation 274 Eq4St 290 lngth 316 St4Eq 361 String entry 363 sub 363 Vec...

Page 278: ...an operation and paste it to the home screen or to a command line in the program editor You also can use the specific keystrokes menus or screens listed in this section Indicates menus or screens that...

Page 279: ...magnitude modulus of complexNumber abs real imaginary returns real2 imaginary2 abs magnitude angle returns magnitude abs L256 4 b 256 4 abs L4 3 13 b 25 abs L4 3 13 b 1 abs 3 4 b 5 abs 3 4 b 3 abs lis...

Page 280: ...ation on page 274 1 2 3 4 5 6 b 5 7 9 1 2 3 4 5 6 4 5 6 7 8 9 b 5 7 9 11 13 15 1 2 3 4 5 6 b 5 7 9 and BASE BOOL menu integerA and integerB Compares two real integers bit by bit Internally both intege...

Page 281: ...mode and PolarC complex number mode angle 3 4 b 927295218002 angle 3 2 b 2 6 p 3 A b 6 1 0471975512 angle A b 1 0471975512 angle complexList angle complexMatrix angle complexVector Returns a list mat...

Page 282: ...use AsmComp to compile the ASCII version once and then execute the hex version each time you want to run the program AsmPrgm CATALOG AsmPrgm Must be used as the first line of an assembly language pro...

Page 283: ...pended as a new column to the end of matrix The arguments can be real or complex The number of rows in matrix must equal the number of elements in vector 1 2 3 4 5 6 MATA b 1 2 3 4 5 6 7 8 9 10 MATB b...

Page 284: ...b 100011 4Bin BASE CONV menu number 4Bin list 4Bin matrix4Bin vector 4Bin Returns the binary equivalent of the real or complex argument In Dec number base mode 2 8 b 16 Ans4Bin b 10000 1 2 3 4 4Bin b...

Page 285: ...2 7 b ClDrw GRAPH DRAW menu STAT DRAW menu ClDrw Clears all drawn elements from the current graph CILCD program editor I O menu ClLCD Clears the home screen LCD ClrEnt MEM menu ClrEnt Clears the cont...

Page 286: ...MATRX MATH menu cond squareMatrix Returns the condition number of a real or complex squareMatrix which is calculated as cnorm squareMatrix cnorm squareMatrixL1 The condition number indicates how well...

Page 287: ...rns real Limaginary In PolarC mode conj magnitude angle returns magnitude Langle Lp angle p conj complexList conj complexMatrix conj complexVector Returns a complex list matrix or vector in which each...

Page 288: ...atrix cannot have repeated eigenvalues cos list Returns a list in which each element is the cosine of the corresponding element in list cos squareMatrix Returns a square matrix that is the matrix cosi...

Page 289: ...osine of the corresponding element in list cosh 0 1 2 b 1 1 81065556732 coshL1 MATH HYP menu coshL1 number or cosL1 expression Returns the inverse hyperbolic cosine of number or expression which can b...

Page 290: ...r q z even if the display mode is not set for cylindrical CylV L2 0 4Cyl b 2 3 14159265359 0 L2 0 1 4Cyl b 2 3 14159265359 1 CylV mode screen CylV Sets cylindrical vector coordinate mode r q z In Cyl...

Page 291: ...gree Sets degree angle mode In Degree angle mode sin 90 b 1 sin p 2 b 027412133592 Degree entry MATH ANGLE menu number or expression Designates a real number or expression as degrees regardless of the...

Page 292: ...pression with respect to variable at the real or complex value der1 x 3 x 5 b 75 der1 expression variable Uses the current value of variable 3 x b 3 der1 x 3 x b 27 der1 expression variable list Retur...

Page 293: ...VECTR OPS menu dim matrix Returns a list containing the dimensions number of rows and columns of a real or complex matrix dim vector Returns the length number of elements of a real or complex vector 2...

Page 294: ...EC b 1 2 3 dim VEC b 3 VEC b 1 2 0 dimL LIST OPS menu dimL list Returns the length number of elements of a real or complex list dimL 2 7 L8 0 b 4 1 dimL 2 7 L8 0 b 25 dimL X then LIST OPS menu ofEleme...

Page 295: ...ogram editor I O menu Disp valueA valueB valueC Displays each value The values can include strings and variable names Disp Displays the home screen 10 x b 10 Disp x 3 3 xN6 b 1024 Done Hello STR b Hel...

Page 296: ...b L8 16666666667 number list or expression list Returns a list in which each element is number or expression divided by the corresponding element in list 100 10 25 2 b 10 4 50 list number or list exp...

Page 297: ...r expressions Do not use and symbols to specify degrees and seconds For example 5 59 is interpreted as implied multiplication of 5 59 according to the current angle mode setting 54 32 30 b 54 54166666...

Page 298: ...Bob Fedorisko Revised 02 13 01 2 42 PM Printed 02 13 01 3 05 PM Page 286 of 118 DrawF GRAPH DRAW menu DrawF expression Draws expression in terms of x on the current graph In Func graphing mode ZStd Dr...

Page 299: ...be stored also After the solution is drawn DrEqu waits for you to move the cursor to a new initial value and press b to draw the new solution You then are prompted to press Y to specify another initi...

Page 300: ...alue for each function in an expression It is more accurate than dxNDer but more restrictive in that only certain functions are valid in the expression The current differentiation type is used by the...

Page 301: ...chniques This is not the same as simply calculating the exponential of each element eigVc MATRX MATH menu The squareMatrix cannot have repeated eigenvalues eigVc squareMatrix Returns a matrix containi...

Page 302: ...6789E6 In Normal notation mode 123456789 b 123456789 Eq4St STRNG menu Eq4St equationVariable stringVariable Converts the contents of equationVariable to a string and stores it to stringVariable Be sur...

Page 303: ...dulus of each element is compared Strings are case sensitive If true argumentA argumentB returns 1 If false argumentA argumentB returns 0 2 2 2 2 b 1 2 2 2 2 b 5 1 2 3N2 L1 3 b 1 A a b 0 listA listB R...

Page 304: ...rns a list containing the values of expression evaluated with respect to variable at each element in list evalF x 3 x 5 x 3 5 b 35 135 Exponent E C number E power or expressionA E expressionB Returns...

Page 305: ...ilt in equation variable such as y1 r1 and xt1 Values used for xList yList and frequencyList are stored automatically to built in variables xStat yStat and fStat respectively The regression equation i...

Page 306: ...ger where 0 integer 449 and 0 non integer 449 9 For a non integer the Gamma function is used to find the factorial An expression must evaluate to an appropriate value 6 b 720 12 5 b 1710542068 32 list...

Page 307: ...h a real or complex number 3 4 5 L1 b 3 4 5 Fill 8 L1 b Done L1 b 8 8 8 Fill 3 4 L1 b Done L1 b 3 4 3 4 3 4 Fix mode screen Fix integer or Fix expression Sets fixed decimal mode for integer number of...

Page 308: ...r upper Returns the value at which a local minimum of expression with respect to variable occurs between real lower and upper bounds for variable The tolerance is controlled by the built in variable t...

Page 309: ...FnOn 1 3 b Done FnOn Selects all equation function numbers FnOn b Done For program editor CTL menu For variable begin end step or For variable begin end loop loop End End commands commands Executes th...

Page 310: ...5 20 L1 b 5 10 15 20 L2 b 50 100 150 200 Form L1 5 L2 b Done L2 b 1 2 3 4 fPart MATH NUM menu fPart number or fPart expression Returns the fractional part of a real or complex number or expression fPa...

Page 311: ...lement is the rational equivalent of the corresponding element in the argument 1 2 1 3 1 6N3 8 L1 b 833333333333 L 208 Ans4Frac b 5 6 L5 24 Func mode screen Func Sets function graphing mode gcd MATH M...

Page 312: ...TOP getKy KEY While KEY 0 getKy KEY End Disp KEY Goto TOP To break the program press and then Goto program editor CTL menu Goto label Transfers branches program control to the label specified by an e...

Page 313: ...is the corresponding element in listB 1 5 9 1 L6 10 b 0 1 0 Greater than or equal to TEST menu numberA numberB or expressionA expressionB Tests whether the condition is true or false The arguments mu...

Page 314: ...3 above 6 animate Depending on the graphing mode some graph styles may not be available In Func graphing mode y1 x sin x b Done GrStl 1 4 b Done ZStd b BASE TYPE menu integer Designates a real intege...

Page 315: ...ument In Bin number base mode 1010 1110 b 10001100 Ans4Hex b 8 100 101 110 4Hex b 4 5 6 Hist STAT DRAW menu Hist xList frequencyList Draws a histogram on the current graph using the real data in xList...

Page 316: ...h at yValue In a ZStd graph screen Horiz 4 5 b IAsk CATALOG IAsk Sets the table so that the user can enter individual values for the independent variable IAuto CATALOG IAuto Sets the table so that the...

Page 317: ...ds If condition is true executes command if true Otherwise skips command if true The condition is true if it evaluates to any nonzero number or false if it evaluates to zero To execute multiple comman...

Page 318: ...if false from Else to End and then continues with the next command following End Program segment If x 0 Then Disp x is negative Else Disp x is positive or zero End imag CPLX menu imag complexNumber Re...

Page 319: ...When entering the response the user should not enter quotation marks To prompt for a number or expression instead of a string use Input InpSt variable Displays as the prompt Program segment InpSt Ent...

Page 320: ...TIN86 Use this CBLGET syntax for both CBL and CBR You can receive data also by using Get as described on page 299 Input CBLGET L1 b Done int MATH NUM menu int number or int expression Returns the larg...

Page 321: ...x2 yValue Interpolates or extrapolates an x value for the specified yValue Notice that points x1 y1 and x2 y2 must be entered as y1 x1 and y2 x2 Using points L4 L7 and 2 6 find the x value at y 10 int...

Page 322: ...ent 1 25 L23 45 L99 5 47 15 MAT b 1 25 L23 45 L99 5 47 15 iPart MAT b 1 L23 L99 47 IS program editor CTL menu IS variable value command if variable value commands Increments variable by 1 If the resul...

Page 323: ...on multiple of two nonnegative integers lcm 5 2 b 10 lcm 6 9 b 18 lcm 18 33 b 198 LCust program editor CTL menu LCust item title item title Loads defines the TIN86 s custom menu which is displayed whe...

Page 324: ...onding element in list 1 1 L6 10 b 0 0 1 listA listB Returns a list of 1s and or 0s to indicate if each element in listA is the corresponding element in listB 1 5 9 1 L6 10 b 0 0 1 Less than or equal...

Page 325: ...on equation is stored to equationVariable which must be a built in equation variable such as y1 r1 and xt1 The equation s coefficients always are stored as a list to built in variable PRegC The number...

Page 326: ...xList yList and frequencyList respectively These built in variables must contain valid data of the same dimension otherwise an error occurs The regression equation is stored to equationVariable and R...

Page 327: ...able such as y1 r1 and xt1 Values used for xList yList and frequencyList are stored automatically to built in variables xStat yStat and fStat respectively The regression equation is stored also to bui...

Page 328: ...VECTR OPS menu li4vc list Returns a vector converted from a real or complex list li4vc 2 7 L8 0 b 2 7 L8 0 ln B ln number or ln expression Returns the natural logarithm of a real or complex number or...

Page 329: ...t in equation variable such as y1 r1 and xt1 Values used for xList yList and frequencyList are stored automatically to built in variables xStat yStat and fStat respectively The regression equation is...

Page 330: ...log list Returns a list in which each element is the logarithm of the corresponding element in list In RectC complex number mode log L3 2 b 47712125472 1 364 LU MATRX MATH menu LU matrix lMatrixName...

Page 331: ...s the larger of two real or complex numbers max 2 3 1 4 b 2 3 max list Returns the largest element in list max 1 9 p 2 e 2 b 9 max listA listB Returns a list in which each element is the larger of the...

Page 332: ...onal characters may not be seen on the menu label valid label to which program execution will branch when the user selects this item Program segment Lbl A Input Radius RADIUS Disp Area is p RADIUS2 Me...

Page 333: ...5 MAT 2 3 b 5 3 1 2 0 4 13 L1 22 Multiplication M numberA numberB Returns the product of two real or complex numbers 2 5 b 10 number list or list number number matrix or matrix number number vector or...

Page 334: ...3 4 5 6 MATB b 1 2 3 4 5 6 MATA MATB b 10 14 18 19 26 33 multR MATRX OPS menu multR number matrix row Returns the result of a row multiplication matrix operation where a The specified row of a real or...

Page 335: ...approximate numerical derivative is the slope of the secant line through the points valueNd f valueNd and value d f value d As the step value d gets smaller the approximation usually gets more accura...

Page 336: ...rm a b c returns a2 b2 c2 norm 3 4 5 b 7 07106781187 norm number or norm expression norm list Returns the absolute value of a real or complex number or expression or of each element in list norm L25 b...

Page 337: ...0 becomes 1 and vice versa for the one s complement For example not 78 78 0000000001001110 1111111110110001 one s complement To find the magnitude of a negative binary number determine its two s comp...

Page 338: ...ment is compared Strings are case sensitive If true argumentA argumentB returns 1 If false argumentA argumentB returns 0 2 2 3 2 b 1 2 2 3 2 b 5 1 2 3N2 L1 3 b 0 A a b 1 listA listB Returns a list of...

Page 339: ...designator respectively from the BASE TYPE menu In Oct number base mode 10 10 10 b 43 4Oct BASE CONV menu number 4Oct list 4Oct matrix4Oct vector 4Oct Returns the octal equivalent of the real or compl...

Page 340: ...menu integerA or integerB Compares two real integers bit by bit Internally both integers are converted to binary When corresponding bits are compared the result is 1 if either bit is 1 the result is 0...

Page 341: ...3 05 PM Page 329 of 118 Outpt program editor I O menu Outpt row column string Displays string beginning at row and column where 1 row 8 and 1 column 21 Outpt row column value Displays value beginning...

Page 342: ...t in variable PRegC Values used for xList yList and frequencyList are stored automatically to built in variables xStat yStat and fStat respectively The regression equation is stored also to built in e...

Page 343: ...nd yList and frequencies in frequencyList The regression equation is stored to equationVariable which must be a built in equation variable such as y1 r1 and xt1 The equation s coefficients always are...

Page 344: ...frequencyList equationVariable Performs a fourth order polynomial regression using real data pairs in xList and yList and frequencies in frequencyList The regression equation is stored to equationVar...

Page 345: ...fStat for xList yList and frequencyList respectively These built in variables must contain valid data of the same dimension otherwise an error occurs The regression equation is stored to equationVaria...

Page 346: ...10 10 5 200 b 30 pEval MATH MISC menu pEval coefficientList xValue Returns the value of a polynomial whose coefficients are given in coefficientList at xValue Evaluate y 2x2 2x 3 at x 5 pEval 2 2 3 5...

Page 347: ...istName and yListName The optional mark specifies the character used to plot the points If you omit mark a box is used mark 1 box 2 cross 3 dot xyLine plot Plot1 2 xListName yListName mark Plot1 2 xLi...

Page 348: ...37 1 570 list 4Pol matrix4Pol vector 4Pol Returns a list matrix or vector in which each element of the argument is displayed in polar form 1 L2 b 1 0 0 1 141421356 Ans4Pol b 1 0 1 4142135623 PolarC mo...

Page 349: ...N14x 20 0 poly 2 L8 L14 20 b 5 L2 1 Power number power or expression expression Returns number raised to power The arguments can be real or complex 4 2 b 16 2 L5 b 03125 listA listB Returns a list in...

Page 350: ...SC menu prod list Returns the product of all real or complex elements in list prod 1 2 4 8 b 64 prod 2 7 L8 b L112 Prompt program editor I O menu Promp shows on menu Prompt variableA variableB Prompts...

Page 351: ...tion variable such as y1 r1 and xt1 Values used for xList yList and frequencyList are stored automatically to built in variables xStat yStat and fStat respectively The regression equation is stored al...

Page 352: ...Off row column Erases the pixel at row column where 0 row 62 and 0 column 126 PxOff 10 95 PxOn GRAPH DRAW menu PxOn row column Draws the pixel at row column where 0 row 62 and 0 column 126 PxOn 10 95...

Page 353: ...real list as radians cos p 2 p r b 0 L1 rand MATH PROB menu rand Returns a random number between 0 and 1 To control a random number sequence first store an integer seed value to rand such as 0 rand Y...

Page 354: ...integer 0 rand randInt 1 10 b 10 randM MATRX OPS menu randM rows columns Returns a rows columns matrix filled with random one digit integers L9 to 9 0 rand randM 2 3 b 4 L2 0 L7 8 8 randNorm MATH PROB...

Page 355: ...adds the picture stored in pictureName real CPLX menu real complexNumber Returns the real part of complexNumber real real imaginary returns real real magnitude angle returns magnitude cos angle In Ra...

Page 356: ...ns4Rec b 2 59807621135 1 5 RectC mode screen RectC Sets rectangular complex number mode real imaginary In RectC complex number mode L2 b 0 1 41421356237 RectGC graph format screen RectGC Displays grap...

Page 357: ...eat N 1 Fact N Fact NN1 N End Disp 6 Fact Return program editor CTL menu Retur shows on menu Return In a subroutine exits the subroutine and returns to the calling program In the main program stops ex...

Page 358: ...L5 6 L7 3 3 9 9 L9 L7 MAT b L5 6 L7 3 3 9 9 L9 L7 rnorm MAT b 25 rnorm vector Returns the largest absolute value or magnitude in a real or complex vector rnorm 15 L18 7 b 18 Root x MATH MISC menu xth...

Page 359: ...000111100001111 0001111000011110 rotL is not valid in Dec number base mode To enter hexadecimal numbers through use the BASE A F menu Do not use 1 to type a letter In Bin number base mode rotL 0000111...

Page 360: ...round vector ofDecimals Returns a list matrix or vector in which each element is the rounded value of the corresponding element in the argument ofDecimals is optional round p 2 ln 2 3 b 3 142 1 414 69...

Page 361: ...on menu Scatter xList yList Draws a scatter plot on the current graph using the real data pairs in xList and yList Scatter Uses the data in built in variables xStat and yStat These variables must con...

Page 362: ...ing which you select a range of data points a Move the cursor to the leftmost left bound point of the range you want to select and press b b Then move the cursor to the rightmost right bound point of...

Page 363: ...nts of step seq x2 x 1 8 2 b 1 9 25 49 seq expression variable begin end Uses a step of 1 seq x2 x 1 8 b 1 4 9 16 25 36 49 6 SeqG graph format screen SeqG Sets sequential graphing format in which sele...

Page 364: ...perFunc xLeft and xRight The shading style is determined by pattern 1 through 4 and patternRes 1 through 8 pattern 1 vertical default 3 negative slope 45 2 horizontal 4 positive slope 45 patternRes re...

Page 365: ...001111000011110 shftL is not valid in Dec number base mode To enter hexadecimal numbers through use the BASE A F menu Do not use 1 to type a letter In Bin number base mode shftL 0000111100001111 b 111...

Page 366: ...0 to indicate the sign of the corresponding element in list sign L3 2 16 8 6 2N8 b L1 1 0 SimulG graph format screen SimulG Sets simultaneous graphing format in which all selected functions are plott...

Page 367: ...781187 In Degree angle mode sin 45 b 707106781187 sin p 2 r b 1 The squareMatrix cannot have repeated eigenvalues sin list Returns a list in which each element is the sine of the corresponding element...

Page 368: ...or complex sinh 1 2 b 1 50946135541 sinh list Returns a list in which each element is the hyperbolic sine of the corresponding element in list sinh 0 1 2 b 0 1 50946135541 sinhL1 MATH HYP menu sinhL1...

Page 369: ...e such as y1 r1 and xt1 The equation s coefficients always are stored as a list to built in variable PRegC iterations is optional it specifies the maximum number of times 1 through 16 the TI 86 will a...

Page 370: ...own to second screen SlpFld In DifEq graphing mode turns on slope fields To turn off direction and slope fields use FldOff Solver t Solver equation variable guess lower upper Solves equation for varia...

Page 371: ...requencyListName Sortx xListName yListName In ascending order of x elements sorts real or complex x and y data pairs and optionally their frequencies in xListName yListName and frequencyListName The l...

Page 372: ...not set for spherical SphereV In RectV vector coordinate mode 0 L1 4Sph b 1 L1 57079632679 1 0 0 L1 4Sph b 1 0 3 14159265359 SphereV m SphereV Sets spherical vector coordinate mode r q f In SphereV v...

Page 373: ...ariable To convert the string and retain the same variable name you can set equationVariable equal to stringVariable 5 x 6 x b ERROR 10 DATA TYPE 5 x St4Eq x x 6 x b 30 Program segment InpSt Enter y1...

Page 374: ...le 10 A 4 A b 40 Hello STR b Hello 1 2 3 L1 b 1 2 3 1 2 3 VEC b 1 2 3 1 2 3 4 5 6 MAT b 1 2 3 4 5 6 StPic GRAPH menu StPic pictureName Stores a picture of the current graph screen to pictureName StReg...

Page 375: ...4 or A 8 To convert between string variables and equation variables use Eq4St and St4Eq as described on pages 290 and 361 respectively Hello STR b Hello Disp STR Jan b Hello Jan Done sub STRNG menu s...

Page 376: ...3 b 4 5 6 sum MATH MISC menu LIST OPS menu sum list Returns the sum of all real or complex elements in list sum 1 2 4 8 b 15 sum 2 7 L8 0 b 1 tan tan angle or tan expression Returns the tangent of an...

Page 377: ...arctangent of the corresponding element in list In Radian angle mode tanL1 0 2 5 b 0 19739555985 463 tanh MATH HYP menu tanh number or tanh expression Returns the hyperbolic tangent of number or expre...

Page 378: ...Radian angle mode ZTrig TanLn cos x p 4 b Text GRAPH DRAW menu Text row column string Writes a text string on the current graph beginning at pixel row column where 0 row 57 and 0 column 123 Text at th...

Page 379: ...ser trace a function From a program press b to stop tracing and continue with the program Transpose T MATRX MATH menu matrixT Returns a transposed real or complex matrix in which element row column is...

Page 380: ...e stored automatically to the built in variables xStat yStat and fStat respectively TwoVar xList yList Uses frequencies of 1 TwoVar Uses xStat yStat and fStat for xList yList and frequencyList These b...

Page 381: ...i 2 7 L8 0 b 2 7 L8 0 vc4li 2 7 L8 0 2 b 4 49 64 0 Vector entry and element1 element2 Defines a vector in which each element is a real or complex number or variable 4 5 6 VEC b 4 5 6 In PolarC complex...

Page 382: ...of the bit results For example 78 xor 23 89 78 1001110 23 0010111 1011001 89 You can enter real numbers instead of integers but they are truncated automatically before the comparison In Dec number ba...

Page 383: ...Chap 20 US English Bob Fedorisko Revised 02 13 01 2 42 PM Printed 02 13 01 3 05 PM Page 371 of 118 ZData GRAPH ZOOM menu ZData Adjusts the window variable values based on the currently defined statist...

Page 384: ...ndow variable values such that x y 1 and then updates the graph screen with the origin centered on the screen xMin L6 3 yMin L3 1 xMax 6 3 yMax 3 1 xScl 1 yScl 1 One of the benefits of ZDecm is that y...

Page 385: ...Recalculates yMin and yMax to include the minimum and maximum y values of the selected functions between the current xMin and xMax and then updates the graph screen This does not affect xMin and xMax...

Page 386: ...that each pixel is an integer in all directions x y 1 sets xScl yScl 10 and then updates the graph screen The current cursor location becomes the center of the new graph One of the benefits of ZInt i...

Page 387: ...3 01 3 05 PM Page 375 of 118 ZOut GRAPH ZOOM menu ZOut Zooms out to display more of the graph centered around the current cursor location Zoom factors are set by the values of built in variables xFact...

Page 388: ...dow variables or Store the applicable values to the zoom window variables whose names begin with z followed by the regular window variable name For example store a value for xMin to zxMin yMin to zyMi...

Page 389: ...andard default values and then updates the graph screen Func graphing mode xMin L10 yMin L10 xMax 10 yMax 10 xScl 1 yScl 1 Pol graphing mode qMin 0 xMin L10 yMin L10 qMax 6 28318530718 2p xMax 10 yMax...

Page 390: ...13 01 3 05 PM Page 378 of 118 ZTrig GRAPH ZOOM menu ZTrig Sets the window variables to preset values appropriate for plotting trig functions in Radian angle mode x p 24 and then updates the graph scr...

Page 391: ...US English Bob Fedorisko Revised 02 27 01 1 20 PM Printed 02 27 01 1 26 PM Page 379 of 26 TI 86 Menu Map 380 Handling a Difficulty 392 Error Conditions 393 Equation Operating System EOS 397 TOL The T...

Page 392: ...r menus the other menus follow directly below the main menu In the program editor the appearance of some menus changes slightly The menu map omits user created name menus such as the LIST NAMES and CO...

Page 393: ...APH 4 MATH DRAW FORMT STGDB RCGDB 4 EVAL STPIC RCPIC GRAPH Menu 6 in DifEq graphing mode Q t WIND INITC AXES GRAPH 4 FORMT DRAW ZOOM TRACE EXPLR 4 EVAL STGDB RCGDB STPIC RCPIC Equation Editor Menu 6 i...

Page 394: ...t 4 FnOn FnOff Axes Q dTime 4 fldRes GRAPH WIND Window Variables Menu 6 in the program editor only y x WIND ZOOM TRACE GRAPH xMin xMax xScl yMin yMax 4 yScl tMin tMax tStep qMin 4 qMax qStep tPlot di...

Page 395: ...RIZ CIRCL 4 DrawF PEN PTON PTOFF PTCHG 4 CLDRW PxOn PxOff PxChg PxTest 4 TEXT TanLn DrInv SOLVER Menu t equation b SOLVER ZOOM Menu t equation b GRAPH WIND ZOMM TRACE SOLVE BOX ZINT ZOUT ZFACT ZSTD TA...

Page 396: ...O CTL INSc 4 DELc UNDEL PRGM I O Input Output Menu 8 program name b PAGE PAGE I O CTL INSc Input Promp Disp DispG DispT 4 ClTbl Get Send getKy ClLCD 4 Outpt InpSt PRGM CTL Control Menu 8 programName...

Page 397: ...RX Menu Matrix Editor Menu matrixName b NAMES EDIT MATH OPS CPLX INSr DELr INSc DELc 4REAL MATRX MATH Menu NAMES EDIT MATH OPS CPLX det T norm eigVl eigVc 4 rnorm cnorm LU cond MATRX OPS Operations Me...

Page 398: ...nted 02 27 01 1 26 PM Page 386 of 26 VECTR OPS Operations Menu NAMES EDIT MATH OPS CPLX dim Fill 4Pol 4Cyl 4Sph 4 4Rec li4vc vc4li VECTR CPLX Menu NAMES EDIT MATH OPS CPLX conj real imag abs angle CPL...

Page 399: ...coshL1 4 tanhL1 MATH MISC Miscellaneous Menu NUM PROB ANGLE HYP MISC sum prod seq lcm gcd 4 4Frac pEval x eval CONS Constants Menu BLTIN EDIT USER CONS BLTIN Built In Constants Menu BLTIN EDIT USER Na...

Page 400: ...V VOL Volume Menu LNGTH AREA VOL TIME TEMP liter gal qt pt oz 4 cm3 in3 ft3 m3 cup 4 tsp tbsp ml galUK ozUK CONV TIME Menu LNGTH AREA VOL TIME TEMP sec mn hr day yr 4 week ms s ns CONV TEMP Temperatur...

Page 401: ...ftlb s cal s Btu m ft s m s mi hr km hr knot STRNG Menu sub lngth Eq4St St4Eq LIST Menu LIST NAMES Menu NAMES EDIT OPS NAMES EDIT OPS fStat xStat yStat List Editor Menu NAMES OPS 4 4REAL LIST OPS Ope...

Page 402: ...ean Menu BASE BIT Menu TYPE CONV BOOL BIT TYPE CONV BOOL BIT and or xor not rotR rotL shftR shftL TEST Relational Menu 4 MEM Memory Menu RAM DELET RESET TOL ClrEnt MEM DELET Delete Menu ALL REAL CPLX...

Page 403: ...T3 PlOn PlOff SCAT xyLINE MBOX HIST BOX Plot Mark Menu or or PLOT1 PLOT2 PLOT3 PlOn PlOff STAT DRAW Menu CALC EDIT PLOT DRAW VARS HIST SCAT xyLINE BOX MBOX 4 DRREG CLDRW DrawF STPIC RCPIC STAT VARS St...

Page 404: ...e and then press and hold If an error menu is displayed follow the steps in Chapter 1 Refer to the Error Conditions section of the Appendix page 393 for details about specific errors if necessary If a...

Page 405: ...range 02 DIV BY ZERO You attempted to divide by zero You attempted a linear regression with a vertical line 03 SINGULAR MAT You attempted to use a singular matrix determinate 0 as the argument for L1...

Page 406: ...an editor you entered a data type that is not allowed check the appropriate chapter You attempted to store data to a protected data type such as a constant program picture or graph database You attemp...

Page 407: ...to instruction label is not defined with a Lbl instruction 23 STAT You attempted a stat calculation with at least one inappropriate list such as a list with less than two data points At least one elem...

Page 408: ...OT MET The algorithm cannot return a result accurate to the requested tolerance 34 STAT PLOT You attempted to display a stat plot that references an undefined list 35 AXES You attempted to plot a DifE...

Page 409: ...ombinations nCr 5th Multiplication implied multiplication and division 6th Addition and subtraction 7th Relational functions such as or 8th Logic operator and 9th Logic operators or and xor Implied Mu...

Page 410: ...follow these open parentheses are specified list elements matrix elements or values for which to solve the equation function TOL The Tolerance Editor On the TI 86 the computational accuracy of some fu...

Page 411: ...I 86 carries more digits internally than it displays Values are stored in memory using up to 14 digits with a 3 digit exponent You can store values up to 12 digits long to most window variables To xSc...

Page 412: ...ge 400 of 26 Support and Service Information Product Support Customers in the U S Canada Puerto Rico and the Virgin Islands For general questions contact Texas Instruments Customer Support phone 1 800...

Page 413: ...01 1 26 PM Page 401 of 26 Product Service Customers in the U S and Canada Only Always contact Texas Instruments Customer Support before returning a product for service Customers outside the U S and C...

Page 414: ...OD TEXAS INSTRUMENTS SHALL NOT BE LIABLE FOR LOSS OF USE OF THE PRODUCT OR OTHER INCIDENTAL OR CONSEQUENTIAL COSTS EXPENSES OR DAMAGES INCURRED BY THE CONSUMER OR ANY OTHER USER Some states provinces...

Page 415: ...ear period Texas Instruments shall not be liable for loss of use of the product or other incidental or consequential costs expenses or damages incurred by the consumer or any other user Some jurisdict...

Page 416: ...PM Printed 02 27 01 1 26 PM Page 404 of 26 99APPX DOC TI 86 Appendix US English Bob Fedorisko Revised 02 27 01 1 20 PM Printed 02 27 01 1 26 PM Page 404 of 26 All Customers outside the U S and Canada...

Page 417: ...wer 48 337 A abs absolute value 49 71 175 185 267 addition 267 ALL 43 232 ALLN 77 ALL 77 ALPHA character 22 ALPHA cursor 22 alpha cursor 22 ALPHA key 21 ALPHA lock 22 44 canceling 22 setting 22 and Bo...

Page 418: ...ter menu 45 CHAR GREEK menu 46 CHAR INTL International menu 46 CHAR MISC Miscellaneous menu 46 characters 19 alpha 22 blue 21 22 case 22 characters continued deleting 23 entering 21 second 22 yellow 2...

Page 419: ...fficient 193 cos cosine 48 186 276 cosL1 arccosine 48 276 cosh hyperbolic cosine 51 277 coshL1 inverse hyperbolic cosine 51 277 CPLX complex number variables 43 71 cross 173 277 cSum cumulative sum 16...

Page 420: ...fferentiation modes 36 difTol tolerance 136 dim dimension 173 184 281 dimL dimension of list 159 282 DirFld direction field 134 282 Disp display 216 283 DispG display graph 283 display 17 display cont...

Page 421: ...ic regression 191 equation variables 40 43 78 equation entry editor 203 equations editing 205 solving 206 error conditions 393 error menu 31 error message 27 error type 27 errors 17 27 correcting 27 d...

Page 422: ...ing with lists 5 161 G gcd greatest common denominator 52 299 GDB graph database 43 GDB variable 102 Get 299 getKy get key 216 300 key code diagram 217 GOTO 26 27 300 Goto PRGM CTL menu 219 224 graph...

Page 423: ...If 218 305 306 imag imaginary 71 175 185 306 imaginary portion of complex number 71 implied multiplication 397 INFLC inflection point 96 97 INITC initial conditions 136 InpSt 217 307 Input PRGM I O m...

Page 424: ...editor 158 storing 154 uses 152 using with function 5 list editor 31 67 156 188 attaching formulas 163 164 removing a list 158 List Editor menu 156 list element complex 156 deleting 158 list element...

Page 425: ...gs 19 20 70 changing 34 displaying 34 number base 65 modulo 49 mRAdd 184 mRAdd 321 multiple entries retrieving 29 multiplication 321 multR multiply row 184 322 N n statistical results variable 193 nat...

Page 426: ...102 pictures recalling 102 saving 102 pixel resolution for function graphs 81 PlOff plot off 195 334 PlOn plot on 195 334 PLOT1 195 Plot1 335 PLOT2 195 Plot2 335 PLOT3 195 Plot3 335 plotting function...

Page 427: ...Q Q n equation variables 135 Qrtl1 193 Qrtl3 193 Quick Zoom 91 in parametric graphing 129 in polar graphing 120 Quick Find Locator A to Z Reference 262 R r radian entry 341 rAdd 184 rAdd 340 Radian an...

Page 428: ...d 216 350 separator 70 seq sequence 52 160 351 SeqG sequential graphing 84 351 series of instructions displaying 18 SetLE 159 SetLEdit 161 351 setting graph format 83 setting graph style 80 Shade 103...

Page 429: ...on 190 362 string 29 concatenating 226 creating 226 defined 226 storing 226 227 string entry 363 STRNG string variables 43 STRNG String menu 227 STYLE 77 sub subset of string 227 363 submatrix display...

Page 430: ...ames 44 recalling 42 storing data to 39 storing results to 3 30 uppercase and lowercase names 39 x variable 77 y variable 77 variable equations in a table 114 VARS CPLX complex variables screen 71 VAR...

Page 431: ...ZOOM menu 92 ZIn zoom in 373 ZIN zoom in 92 208 ZInt 374 ZINT GRAPH ZOOM menu 92 ZOOM 14 75 88 custom 93 parametric graphs 129 polar graphs 121 ZOOM operations 147 zoom window variables storing and r...

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