Texas Instruments TI-36X Pro Page 53 User Manual Download

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Matrix example

Define matrix [A] as

Calculate the determinant, transpose, inverse, and rref of [A].

Define [A]

Set

dimensions

< " <

Enter

values

det([A])

<
%

< )

Transpose

Inverse

-
%

"$$

1 2
3 4

Summary of Contents for TI-36X Pro

Page 1: ...Answer toggle 10 Last answer 10 Order of operations 11 Clearing and correcting 13 Fractions 13 Percentages 15 EE key 16 Powers roots and inverses 17 Pi 18 Math 19 Number functions 20 Angles 21 Rectan...

Page 2: ...any programs or book materials and makes such materials available solely on an as is basis In no event shall Texas Instruments be liable to anyone for special collateral incidental or consequential d...

Page 3: ...ned Display contrast The brightness and contrast of the display can depend on room lighting battery freshness and viewing angle To adjust the contrast 1 Press and release the key 2 Press T to darken t...

Page 4: ...See Mode section DEG RAD GRAD Angle mode degrees radians or gradians See Mode section L1 L2 L3 Displays above the lists in data editor H B O Indicates HEX BIN or OCT number base mode No indicator disp...

Page 5: ...a mode and to select it Press or s to return to the Home screen and perform your work using the chosen mode settings Default settings are highlighted in these sample screens DEG RAD GRAD Sets the ang...

Page 6: ...Sets the decimal notation mode FLOAT floating decimal point displays up to 10 digits plus the sign and decimal 0 1 2 3 4 5 6 7 8 9 fixed decimal point specifies the number of digits 0 through 9 to dis...

Page 7: ...mode MathPrint mode Sci Sci Float mode and answer toggle key Float mode and answer toggle key Fix 2 Fix 2 and answer toggle key U n d U n d Exponent example Exponent example Square root example Square...

Page 8: ...sections of this guidebook describe how to use the keys Menus Menus give you access to a large number of calculator functions Some menu keys such as h display a single menu Others such as d display m...

Page 9: ...n expression the expression and its result are added automatically to the history Use and to scroll through the history You can reuse a previous entry by pressing to paste it on the bottom line where...

Page 10: ...ed value which may not match the rounded value Example Last answer i The last entry performed on the home screen is stored to the variable ans This variable is retained in memory even after the calcul...

Page 11: ...hat are entered after the argument such as x2 and angle unit modifiers 5th Exponentiation and roots x Note In Classic mode exponentiation using the G key is evaluated from left to right The expression...

Page 12: ...Multiplication implied multiplication division 9th Addition and subtraction 10th Conversions n d Un d F D 4DMS 11th completes all operations and closes all open parentheses Q P M 6 0 T 5 V M1 2 M 1 T...

Page 13: ...ominator must be a positive integer To compute more complex expressions functions variables complex numbers etc use W along with and The calculator defaults output to improper fractions Results are au...

Page 14: ...limit places the cursor in the history Pressing enter will then paste the expression back to that MathPrint level To paste a previous entry in the denominator place the cursor in the denominator pres...

Page 15: ...alculation involving a percentage press _ after entering the value of the percentage Example F D 4 1 P 2 n d U n d P3 4 T 1 7 12 n d Un d 9 P 2 d 1 F D 4 1 2 Examples MathPrint mode only P1 2 T 1 3 4...

Page 16: ...on figures what is the total quantity of metal obtained If one ton of metal is worth 280 dollars what is the total value of the metal extracted The two extractions represent a total of 317 9 tons of m...

Page 17: ...to the power indicated Use to move the cursor out of the power b Calculates the square root of a non negative value c Calculates the nth root of any non negative value and any odd integer root of a ne...

Page 18: ...41592654 for display Example Problem What is the area of a circle if the radius is 12 cm Reminder A p r2 The area of the circle is 144 p square cm The area of the circle is approximately 452 4 square...

Page 19: ...rts between simple fractions and mixed number form 2 lcm Least common multiple 3 gcd Greatest common divisor 4 4Pfactor Prime factors 5 sum Summation 6 prod Product n d Un d 9 P 2 d 1 lcm d 2 6 9 gcd...

Page 20: ...part of a number 4 fPart Fractional part of a number 5 int Greatest integer that is the number 6 min Minimum of two numbers 7 max Maximum of two numbers 8 mod Modulo remainder of first number P secon...

Page 21: ...or GRAD Entries are interpreted and results displayed according to the angle mode setting without needing to enter an angle unit modifier Examples mod d 8 17 12 6 1 Specifies the angle unit modifier a...

Page 22: ...und the results to two decimal places The result is 39 degrees 26 minutes and 23 seconds Problem It is known that 30 p 6 radians In the default mode degrees find the sine of 30 Then set the calculator...

Page 23: ...and polar r q format Set Angle mode as necessary before starting calculations Example Convert polar coordinates r q 5 30 into rectangular coordinates Then convert rectangular coordinates x y 3 4 into...

Page 24: ...ti tap keys Enter trigonometric functions sin cos tan sin 1 cos 1 tan 1 just as you would write them Set the desired Angle mode before starting trigonometric calculations Example Degree Mode Example R...

Page 25: ...n calculate angle B and the length of the hypotenuse c Lengths are in meters Round results to one decimal place Reminder tan 1 Z Z1 r cos 5 V Y g P 4 r tan A therefore m A tan 1 m A m B 90 180 therefo...

Page 26: ...hypotenuse is 7 6 meters Hyperbolics X Y Z multi tap keys Pressing one of these multi tap keys repeatedly lets you access the corresponding hyperbolic or inverse hyperbolic function Angle modes do not...

Page 27: ...raises e to the power you specify C C raises 10 to the power you specify Examples Numeric derivative A A calculates an approximate derivative of expression with respect to variable given the value at...

Page 28: ...approximation usually becomes more accurate In MathPrint mode the default H is 1EM3 You can switch to Classic mode to change H for investigations You can use nDeriv once in expression Because of the m...

Page 29: ...umeric function integral of an expression with respect to a variable x given a lower limit and an upper limit Example in RAD angle mode Problem Find the area under the curve f x Mx2 4 from M2 to 0 and...

Page 30: ...peration To set an operation and then recall it 1 Press n 2 Enter any combination of numbers operators and or values up to 44 characters 3 Press to store the operation 4 Press m to recall the stored o...

Page 31: ...expression result to a memory variable Features of the calculator that use variables such as the solvers will use the values that you store L lets you store values to variables Press L to store a var...

Page 32: ...ssion To enter two or more variables in succession press after each h recalls the values of variables Press h to display a menu of variables and their stored values Select the variable you want to rec...

Page 33: ...meters by 560 meters the second one measures 340 meters by 610 meters What volume of gravel does the company need to extract from each excavation to reach a depth of 150 meters To reach 210 meters Dis...

Page 34: ...s and to extract 43 554 million cubic meters to reach a depth of 210 meters Data editor and list formulas v v lets you enter data in up to 3 lists Each list can contain up to 42 items Press to go to t...

Page 35: ...is the result of a formula Problem On a November day a weather report on the Internet listed the following temperatures Paris France 8 C Moscow Russia M1 C Montreal Canada 4 C Convert these temperatur...

Page 36: ...formation along with the 2 Var statistics for the data in StatVars menu item 1 v 1 9 W 5 V v 1 T 32 21 1 StatVars Displays a secondary menu of statistical result variables Use and to locate the desire...

Page 37: ...At least three data points are required 6 CubicReg Fits the third degree polynomial y ax3 bx2 cx d to the data It displays values for a b c and d it also displays a value for R2 For four points the e...

Page 38: ...9 represents Minfinity to infinity 3 invNorm Computes the inverse cumulative normal distribution function for a given area under the normal distribution curve specified by mean mu and standard deviati...

Page 39: ...probability at x for the discrete binomial distribution with the specified numtrials and probability of success p on each trial x can be non negative integer and can be entered with options of SINGLE...

Page 40: ...5 To clear data press v v select a list to clear and press sx or sy Population standard deviation of x or y Gx or Gy Sum of all x or y values Gx2 or Gy2 Sum of all x2 or y2 values Gxy Sum of x y for...

Page 41: ...1 Var Example Find the mean of 45 55 55 55 2 Var Example Data 45 30 55 25 Find x 45 Clear all data v v Data 45 55 55 55 Stat s u 2 Selects 1 Var Stats Stat Var 2 V 2 Clear all data v v Data 45 55 30...

Page 42: ...ge 2 What does the value of n given by the calculator represent What does the value of Gx given by the calculator represent Reminder The weighed average is 3 The teacher gave Anthony 4 more points on...

Page 43: ...sents the total sum of the weights n 1 0 5 1 0 5 Gx represents the weighted sum of his scores 12 1 13 0 5 10 1 11 0 5 34 Change Anthony s last score from 11 to 15 If the teacher adds 4 points to Test...

Page 44: ...eling at 55 kph A hand drawn scatter plot of these data points suggest a linear relationship The calculator uses the least squares method to find the line of best fit y ax b for data entered in lists...

Page 45: ...s for a vehicle traveling at 55 kph Regression example 1 Calculate an ax b linear regression for the following data 1 2 3 4 5 5 8 11 14 17 Regression example 2 Calculate the exponential regression for...

Page 46: ...4 Data 0 1 2 3 4 10 14 23 35 48 Regression u Save the regression equation to f x in the I menu Regression Equation Find the average value y of the data in L2 using StatVars u 1 Selects StatVars Notice...

Page 47: ...ther regression calculation if you want to preserve your regression coefficients a b c d and r values for your particular problem in the StatVars menu Distribution example Compute the binomial pdf dis...

Page 48: ...rder of objects is not important as in a hand of cards nPr Calculates the number of possible permutations of n items taken r at a time given n and r The order of objects is important as in a race rand...

Page 49: ...n choose from 2300 dishes with different combinations of flavors If a long hot summer is about 90 days long you will need to eat about 25 ice cream dishes each day Function table I displays a menu wit...

Page 50: ...minder The vertex of the parabola is the point on the parabola that is also on the line of symmetry 2 Edit function Lets you define the function f x and generates a table of values Start Specifies the...

Page 51: ...4 Problem A charity collected 3 600 to help support a local food kitchen 450 will be given to the food kitchen every month until the funds run out How many months will the charity support the kitchen...

Page 52: ...lays the matrix MATH menu which lets you perform the following operations t EDIT t displays the matrix EDIT menu which lets you define or edit matrix A B or C 1 A Definable matrix A 2 B Definable matr...

Page 53: ...53 Matrix example Define matrix A as Calculate the determinant transpose inverse and rref of A Define A t Set dimensions Enter values 1 2 3 4 det A t t Transpose t t Inverse t t 1 2 3 4...

Page 54: ...r will be interpreted as a column vector NAMES displays the vector NAMES menu which shows the dimensions of the vectors and lets you use them in calculations rref t t Notice that A has an inverse and...

Page 55: ...fine or edit vector u v or w Vector example Define vector u 0 5 8 Define vector v 2 3 Calculate u v DotP u v and norm v 1 DotProduct Syntax DotP vector1 vector2 Both vectors must be the same dimension...

Page 56: ...nd the values of the variables You then select which variable to solve for The equation is limited to a maximum of 40 characters Add vectors T DotP 5 V 2 T 8 V 3 Note DotP is calculated here in two wa...

Page 57: ...quation solver You then enter the coefficients of the variables and solve Num solv Left side 1 P2 zF U5 z z z z z Right side 6 z U z z zz z z Variable values 1 P 2 2 P 3 0 25 Solve for b Note Left Rig...

Page 58: ...se values On the solution screens of the polynomial solver you can press r to toggle the number format of the solutions x1 x2 and x3 Poly solv Enter coefficients 1 M 2 2 Solutions Note If you choose t...

Page 59: ...to toggle the results x y and z as needed The 2x2 equation solver solves for a unique solution or displays a message indicating an infinite number of solutions or no solution The 3x3 system solver so...

Page 60: ...60 Example 3 3 system Solve 5x 2y 3z 9 4x 3y 5z 4 2x 4y 2z 14 Toggle result type r System solve 3 3 system First equation 5 M2 3 M 9 Second equation 4 3 5 4 Third equation 2 4 M2 14 Solutions...

Page 61: ...e displays the TYPE menu which lets you designate the base of a number regardless of the calculator s current number base mode Enter the system 2 1 2 3 4 2 4 6 8 3 6 9 12 1 Hex Converts to hexadecimal...

Page 62: ...ean logic 3 d Specifies a decimal number 4 o Specifies an octal integer d Hex 127 1 h Bin 1 2 b Oct 10000000 2 4 o Dec 1 and Bitwise AND of two integers 2 or Bitwise OR of two integers 3 xor Bitwise X...

Page 63: ...essing from a populated home screen expression pastes the content to Expr If the user is in an input or output history line when is pressed the home screen expression pastes to Expr Example BIN mode a...

Page 64: ...to select either the NAMES or UNITS menus of the same 20 physical constants Use and to scroll through the list of constants in the two menus The NAMES menu displays an abbreviated name next to the ch...

Page 65: ...0M27 kilograms mn neutron mass 1 674927211 10M27 kilograms m muon mass 1 88353130 10M28 kilograms G universal gravitation 6 67428 10M11 meters3 per kilogram per seconds2 F Faraday constant 96485 3399...

Page 66: ...and Length Pressure and Power and Energy English Metric conversion Conversion in 4 cm inches to centimeters cm 4 in centimeters to inches ft 4 m feet to meters m 4 ft meters to feet yd 4 m yards to me...

Page 67: ...hr 4 m s kilometers hour to meters second m s 4 km hr meters second to kilometers hour LtYr 4 m light years per meter m 4 LtYr meters to light years pc 4 m parsecs to meters m 4 pc meters to parsecs A...

Page 68: ...Pa atmospheres to Pascals Pa 4 atm Pascals to atmospheres mmHg 4 kPa millimeters of mercury to Pascals Pa 4 mmHg Pascals to millimeters of mercury Temperature M22 2 Enclose negative numbers expression...

Page 69: ...bi or r q and press REAL a bi or r q set the format of complex number results a bi rectangular complex results r q polar complex results Notes Complex results are not displayed unless complex numbers...

Page 70: ...p Displays a complex result in polar form Valid only at the end of an expression Not valid if the result is real 5 4 a bi Displays a complex result in rectangular form Valid only at the end of an exp...

Page 71: ...error message The previous screen is displayed with the cursor at or near the error location Correct the expression The following list includes some of the errors that you may encounter 0 area 1 This...

Page 72: ...real number is required You attempted to store an incorrect data type such as a matrix to a list Input to the complex conversions is real You attempted to execute a complex number in an area that is...

Page 73: ...a in a Polynomial solver calculation is pre populated with zero or if the you set a to zero and you move the cursor to the next input line Infinite Solutions The equation entered in the System of lin...

Page 74: ...o sign change Change guess The Numeric equation solver did not detect a sign change No Solution Found The equation entered in System of linear equations solver has no solution Number of trials 0 n 41...

Page 75: ...placed functions arguments parentheses or commas If using P try using W and the appropriate parentheses TOL NOT MET You requested a tolerance to which the algorithm cannot return an accurate result TO...

Page 76: ...l Do not mutilate puncture or dispose of batteries in fire The batteries can burst or explode releasing hazardous chemicals Discard used batteries according to local regulations How to remove or repla...

Page 77: ...his unit Perchlorate Material Special handling may apply See www dtsc ca gov hazardouswaste perchlorate In case of difficulty Review instructions to be certain calculations were performed properly Che...

Page 78: ...ce All other customers Refer to the leaflet enclosed with this product hardware or contact your local Texas Instruments retailer distributor Home Page education ti com KnowledgeBase and e mail inquiri...

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