Summary of Contents

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TI36X Pro Calculator Important information............. 2 Examples ................3 Switching the calculator on and off ........3 Display contrast ..............3 Home screen ................. 3 2nd functions ................. 5 Modes ..................5 Multitap keys................. 8 Menus ..................8 Scrolling expressions and history .......... 9 Answer toggle..............

Page 2: Table Of Contents
Texas Instruments, regardless of the form of action, shall not exceed the purchase price of this product.

Page 3: Examples, Switching The Calculator On And Off, Display Contrast, Home Screen
On the Home screen, you can enter mathematical expressions and functions, along with other instructions. The answers are displayed on the Home screen. The TI36X Pro screen can display a maximum of four lines with a maximum of 16 characters per line. For entries and expressions of more than 16 characters, you can scroll left and right (!and ") to...

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When you calculate an entry on the Home screen, depending upon space, the answer is displayed either directly to the right of the entry or on the right side of the next line. Special indicators and cursors may display on the screen to provide additional information concerning functions or results.

Page 5: Nd Functions, Modes
Indicator Definition MathPrint™ cursor. Continue entering the current MathPrint™ element, or press an arrow key to exit the element. 2nd functions Most keys can perform more than one function. The primary function is indicated on the key and the secondary function is displayed above it.

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SCI expresses numbers with one digit to the left of the decimal and the appropriate power of 10, as in 1.2345678 5 (which is the same as 1.2345678×10 ENG displays results as a number from 1 to 999 times 10 to an integer power.

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Examples of Classic and MathPrint™ modes Classic mode MathPrint™ mode Float mode and answer Float mode and answer toggle toggle key. key. Fix 2 Fix 2 and answer toggle key. U n/d U n/d Exponent example Exponent example Square root example Square root example Cube root example Cube root example...

Page 8: Multitap Keys, Menus
Multitap keys A multitap key is one that cycles through multiple functions when you press it. For example, the X key contains the trigonometry functions sin and sin as well as the hyperbolic functions sinh and sinh . Press the key repeatedly to display the function that you want to enter.

Page 9: Scrolling Expressions And History
d (key with multiple menus): MATH R ³´ P 1: abs( 1: ¡ 1: P ´Rx( ³´U 2: lcm( 2: round( 2: ¢ 2: P ´Ry( 3: gcd( 3: iPart( 3: £ 3: R ´Pr( 4: 4Pfactor 4: fPart( 4: r 4: R ´Pq( 5: sum( 5: int(...

Page 10: Answer Toggle, Last Answer
Answer toggle Press the r key to toggle the display result (when possible) between fraction and decimal answers, exact square root and decimal, and exact pi and decimal. Pressing r displays the last result in the full precision of its stored value, which may not match the rounded value.

Page 11: Order Of Operations
3 % c % i < Order of operations The TI36X Pro calculator uses Equation Operating System (EOS™) to evaluate expressions. Within a priority level, EOS evaluates functions from left to right and in the following order. Expressions inside parentheses.

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Permutations (nPr) and combinations (nCr). Multiplication, implied multiplication, division. Addition and subtraction. 10th Conversions (n/d³´Un/d, F³´D, 4DMS). 11th < completes all operations and closes all open parentheses. Examples + Q P M 6 0 T 5 V M1 2 < 1 T M 8 T 1 2 <...

Page 13: Clearing And Correcting, Fractions
Clearing and correcting Returns to the Home screen. Clears an error message. Clears characters on entry line. Moves the cursor to last entry in history once display is clear. Deletes the character at the cursor. Inserts a character at the cursor. Clears variables x, y, z, t, a, b, c, and d to their default value of 0.

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• P enters a simple fraction. Pressing P before or after a number can result in different behavior. Entering a number before pressing P makes that number the numerator. To enter fractions with operators or radicals, press P before you enter a number (in MathPrint™ mode only). •...

Page 15: Percentages
F³´D 4 % @ 1 P 2 % ˜ < Examples MathPrint™ mode n/d, U n/d P3 $ 4 " T 1 % @ 7 $12 < 9 P 2 " d 1 < ³´U F³´D 4 % @ 1 $ 2 " % ˜...

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³ Problem A mining company extracts 5000 tons of ore with a concentration of metal of 3% and 7300 tons with a concentration of 2.3%. On the basis of these two extraction 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? 3 % _ V 5000 <...

Page 17: Powers, Roots And Inverses
Powers, roots and inverses Calculates the square of a value. The TI36X Pro calculator evaluates expressions entered with F and a from left to right in both Classic and MathPrint™ modes. Raises a value to the power indicated. Use "...

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2 % a < g (multitap key) p = 3.141592653590 for calculations. p = 3.141592654 for display. Example 2 V g < ³ Problem What is the area of a circle if the radius is 12 cm? Reminder: A = p×r g V 12 F <...

Page 19: Math
Math d MATH d displays the MATH menu: Converts between simple fractions and ³´U mixednumber form. 2: lcm( Least common multiple 3: gcd( Greatest common divisor 4: 4Pfactor Prime factors 5: sum( Summation 6: prod( Product Examples 9 P 2 " d 1 < ³´U lcm( 6 % ` 9 ) <...

Page 20: Number Functions
Number functions d NUM d " displays the NUM menu: 1: abs( Absolute value 2: round( Rounded value 3: iPart( Integer 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(...

Page 21: Angles
mod( d "8 17 % ` 12 ) < ## < !! 6 < Angles d DMS d " " displays the DMS menu: 1: ¡ Specifies the angle unit modifier as degrees (º). 2: ¢ Specifies the angle unit modifier as minutes ('). 3: £...

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q< 2 g d " " 4 < 1.5 d " " 6 < 4DMSS ³ Problem Two adjacent angles measure 12¡ 31¢ 45£ and 26¡ 54¢ 38£ respectively. Add the two angles and display the result in DMS format. Round the results to two decimal places. q$$"""<...

Page 23: Rectangular To Polar
Note: Press  to clear the screen between problems.  X 30 ) < q " <  X g P 6 " ) < Retain radian mode on the calculator and calculate the sine of 30¡. Change the calculator to degree mode and find the sine of p / 6 radians.

Page 24: Trigonometry
 d ! 1 5 % ` 30 ) < d ! 2 5 % ` 30 ) < d !3 3 % ` 4 ) < d ! 4 3 % ` 4 ) < Converting (r, q) = (5, 30) gives (x, y) = (4.3, 2.5) and (x, y) = (3, 4) gives (r, q) = (5.0, 53.1).

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Z Z1 ) < 5 V Y g P 4 " ) < ³ Problem Find angle A of the right triangle below. Then calculate angle B and the length of the hypotenuse c. Lengths are in meters. Round results to one decimal place. Reminder: ⎛...

Page 26: Hyperbolics
90 U % i < % b 3 F T 7 F < To one decimal place, the measure of angle A is 66.8¡, the measure of angle B is 23.2¡, and the length of the hypotenuse is 7.6 meters. Hyperbolics Z (multitap keys) Pressing one of these multitap keys repeatedly lets you...

Page 27: Logarithm And Exponential Functions, Numeric Derivative
Logarithm and exponential functions C (multitap keys) D yields the logarithm of a number to the base e (e ≈ 2.718281828459). D D yields the common logarithm of a number. C raises e to the power you specify. C C raises 10 to the power you specify. Examples D D1 ) <...

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Example in MathPrint™ mode % A % A z F T 5 z "" M 1 < Example in Classic mode Classic: nDeriv(expression,variable,value[ % A % A z F T 5 z %`M1 ) < nDeriv( uses the symmetric difference quotient method, which approximates the numerical derivative value as the slope of the secant line through these points.

Page 29: Numeric Integral
q $$ """" < z G 3 " U 4 z "" 2 P % b 3 <   The slope of the tangent line at x = is zero. A maximum or minimum of the function must be at this point! Numeric integral % Q calculates the numeric function integral of an expression with respect to a variable x, given a lower limit and...

Page 30: Stored Operations
< Notice that both areas are equal. Since this is a parabola with the vertex at (4,0) and zeros at (M2, 0) and (2, 0) you see that the symmetric areas are equal. Stored operations % n lets you store a sequence of operations. % m plays back the operation.

Page 31: Memory And Stored Variables
M 1 % m Memory and stored variables The TI36X Pro calculator has 8 memory variables—x, y, z, t, a, b, c, and d. You can store a real or complex number or an expression result to a memory variable.

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z is a multitap key that cycles through the variable names x, y, z, t, a, b, c, and d. You can also use z to recall the stored values for these variables. The name of the variable is inserted into the current entry, but the value assigned to the variable is used to evaluate the expression.

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L z z < < W 4 < ³ Problem In a gravel quarry, two new excavations have been opened. The first one measures 350 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? Display the results in engineering notation.

Page 34: Data Editor And List Formulas
210 V % h < < 150 V z z < 210 V z z < For the first excavation: The company needs to extract 29.4 million cubic meters to reach a depth of 150 meters, and to extract 41.16 million cubic meters to reach a depth of 210 meters.

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< v < % ˜ < Notice L2 is calculated using the formula you entered, and L2(1)= in the author line is highlighted to indicate the list is the result of a formula. ³ Problem On a November day, a weather report on the Internet listed the following temperatures.

Page 36: Statistics, Regressions, And Distributions
v " 1 9 W 5 V v 1 T 32 < If Sydney, Australia is 21¡C, find the temperature in degrees Fahrenheit. ! $ $ $ 21 < Statistics, regressions, and distributions v lets you enter and edit the data lists. % u displays the STATREG menu, which has the following options.

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3: 2Var Stats Analyzes paired data from 2 data sets with 2 measured variables—x, the independent variable, and y, the dependent variable. Frequency data may be included. Note: 2Var Stats also computes a linear regression and populates the linear regression results. 4: LinReg ax+b Fits the model equation y=ax+b to the data using a leastsquares fit.

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% u " displays the DISTR menu, which has the following distribution functions: 1: Normalpdf Computes the probability density function (pdf) for the normal distribution at a specified x value. The defaults are mean mu=0 and standard deviation sigma=1. The probability density function (pdf) is: 2: Normalcdf Computes the normal distribution probability...

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5: Binomcdf Computes a cumulative 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, LIST or ALL (a list of cumulative probabilities is returned.) 0 { p { 1 must be true.

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sx or sy Population standard deviation of x or y. Gx or Gy Sum of all x or y values. or Gy Sum of all x or y values. Sum of (x…y) for all xy pairs. a (2Var) Linear regression slope. b (2Var) Linear regression yintercept.

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1Var Example Find the mean of {45, 55, 55, 55} Clear all v v $ $ $ data Data < 45 $ 55 $ 55 $ 55 < Stat 2 (Selects 1Var Stats) < Stat Var 2 < V 2 < 2Var Example Data: (45,30);...

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Stat 3 (Selects 2Var Stats) $ $ $ < % s % u 1 # # # # # # < 45 ) < ³ Problem For his last four tests, Anthony obtained the following scores. Tests 2 and 4 were given a weight of 0.5, and tests 1 and 3 were given a weight of 1.

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< v " $ $ $ $ < 12 $ 13 $ 10 $ 11 $ " 1 $ .5 $ 1 $ .5 < 2 (Selects 1Var Stats) $ " " < < Anthony has an average (v) of 11.33 (to the nearest hundredth).

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³ Problem The table below gives the results of a braking test. Test No. Speed (kph) Braking 5.30 14.45 20.21 38.45 distance Use the relationship between speed and braking distance to estimate the braking distance required for a vehicle traveling at 55 kph.

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This line of best fit, y'=0.67732519x'N18.66637321 models the linear trend of the data. Press $ until y' is highlighted. < 55 ) < The linear model gives an estimated braking distance of 18.59 meters 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};...

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L1 = {0, 1, 2, 3, 4}; L2 = {10, 14, 23, 35, 48} Find the average value of the data in L2. Compare the exponential regression values to L2. Clear all data v v 4 Data 0 $1 $ 2 $ 3 $ 4 $ "10 $ 14 $ 23 $ 35 $ 48 <...

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< 0 < 1 < << Warning: If you now calculate 2Var Stats on your data, the variables a and b (along with r and r ) will be calculated as a linear regression. Do not recalculate 2Var Stats after any other 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.

Page 48: Probability
< Probability % † H is a multitap key that cycles through the following options: A factorial is the product of the positive integers from 1 to n. n must be a positive whole number { 69. Calculates the number of possible combinations of n items taken r at a time, given n and r.

Page 49: Function Table
8 H H H 3 < STO 4 rand 5 L % † 1 (Selects rand) < Rand % † 1 < Randint( % † 2 3 % ` 5 ) < ³ Problem An ice cream store advertises that it makes 25 flavors of home made ice cream.

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2: Edit function Lets you define the function f(x) and generates a table of values. The function table allows you to display a defined function in a tabular form. To set up a function table: 1. Press I and select Edit function. 2.

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< After searching close to x = 18, the point (18, 324) appears to be the vertex of the parabola since it appears to be the turning point of the set of points of this function. To search closer to x = 18, change the Step value to smaller and smaller values to see points closer to (18, 324).

Page 52: Matrices
Matrices In addition to those in the Matrix MATH menu, the following matrix operations are allowed. Dimensions must be correct: • matrix + matrix • matrix – matrix • matrix × matrix • Scalar multiplication (for example, 2 × matrix) •...

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Matrix example Define matrix [A] as Calculate the determinant, transpose, inverse, and rref of [A]. Define [A] % t ! < " < " < dimensions < Enter < values 1 $ 2 $ 3 $ 4 $ det([A]) % t " <...

Page 54: Vectors
< rref % t " # < % t <) < Notice that [A] has an inverse and that [A] is equivalent to the identity matrix. Vectors In addition to those in the Vector MATH menu, the following vector operations are allowed. Dimensions must be correct: •...

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% … MATH % … " displays the vector MATH menu, which lets you perform the following vector calculations: 1: DotProduct Syntax: DotP(vector1, vector2) Both vectors must be the same dimension. 2: CrossProduct Syntax: CrossP(vector1, vector2) Both vectors must be the same dimension.

Page 56: Solvers
vectors % … < % … $ < < DotP % … " < % … < % … $ < ) < .5 V 2 T 8 V 3 < Note: DotP is calculated here in two ways. norm % …"...

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Example Reminder: If you have already defined variables, the solver will assume those values. Numsolv % ‰ Left side 1 P2 " zF U5 z z z z z "" Right side 6 z U z z zz z z <...

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Example of quadratic equation Reminder: If you have already defined variables, the solver will assume those values. Polysolv % Š Enter < coefficients < Solutions < Note: If you choose to store the polynomial to f(x), you can use I to study the table of values.

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System of linear equations solver % ‹ % ‹ solves systems of linear equations. You choose from 2×2 or 3×3 systems. Notes: • x, y, and z results are automatically stored in the x, y, and z variables. • Use r to toggle the results (x, y and z) as needed. •...

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Toggle result type Example 3×3 system Solve: 5x – 2y + 3z = 9 4x + 3y + 5z = 4 2x + 4y – 2z = 14 System % ‹ $ solve 3×3 < system First 5 < equation M2 <...

Page 61: Number Bases
Example 3×3 system with infinite solutions Enter the % ‹ 2 system 1 <2 <3 <4 < 2 <4 <6 <8 < 3 <6 <9 <12 < < < < Number bases % — Base conversion % — displays the CONVR menu, which converts a real number to the equivalent in a specified base.

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3: d Specifies a decimal number. 4: o Specifies an octal integer. Examples in DEC mode Note: Mode can be set to DEC, BIN, OCT, or HEX. See the Mode section. d ´Hex 127 % — 1 < h ´Bin % ¬...

Page 63: Expression Evaluation
Examples BIN mode: q $$$$ and, or "" < 1111 % — ! 1 1010 < 1111 % — ! 2 1010 < BIN mode: 11111 % — ! 3 xor, xnor 10101 < 11111 % — ! 4 10101 < HEX mode: q $$$$ not, 2’s...

Page 64: Constants
Constants Constants lets you access scientific constants to paste in various areas of the TI36X Pro calculator. Press % Œ to access, and ! oro" 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.

Page 65
Note: Displayed constant values are rounded. The values used for calculations are given in the following table. Constant Value used for calculations speed of light 299792458 meters per second gravitational 9.80665 meters per second acceleration Planck’s constant 6.62606896×10 Joule seconds NA Avogadro’s number 6.02214179×10 molecules per mole...

Page 66: Conversions
Conversions The CONVERSIONS menu permits you to perform a total of 20 conversions (or 40 if converting both ways). To access the CONVERSIONS menu, press % –. Press one of the numbers (15) to select, or press # and $ to scroll through and select one of the CONVERSIONS submenus.

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lb 4 kg pounds to kilograms kg 4 lb kilograms to pounds Temperature conversion Conversion Farenheit to Celsius ¡ ¡ Celsius to Farenheit ¡ ¡ Celsius to Kelvin ¡ ¡ Kelvin to Celsius ¡ ¡ Speed and length conversion Conversion km/hr 4 m/s kilometers/hour to meters/second m/s 4 km/hr...

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Pressure conversion Conversion atm 4 kPa 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 Examples Temperature %– << (Enclose negative numbers/expressions in parentheses.) Speed, Length –$$<...

Page 69: Complex Numbers
Complex numbers %ˆ The calculator performs the following complex number calculations: • Addition, subtraction, multiplication, and division • Argument and absolute value calculations • Reciprocal, square, and cube calculations • Complex Conjugate number calculations Setting the complex format: Set the calculator to DEC mode when computing with complex numbers.

Page 70
Complex menu Description 1:± ± (polar angle character) Lets you paste the polar representation of a complex number (such as 5±p). 2 :polar angle angle( Returns the polar angle of a complex number. 3: magnitude abs( (or þ in MathPrint™ mode) Returns the magnitude (modulus) of a complex number.

Page 71: Errors
4 r±q 3 T 4 ggg % ˆ 4 < 4 a+bi 5 %ˆ< 3 g P 2 " % ˆ5 < Conjugate: conj( % ˆ6 5 U 6 ggg ) < Real: real( % ˆ7 5 U 6 ggg) <...

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BREAK — You pressed the & key to stop evaluation of an expression. CHANGE MODE to DEC — Base n mode: This error is displayed if the mode is not DEC and you press ‰, Š, ‹, ‡, I, t, …, or –.

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• For TAN: x = 90¡, 90¡, 270¡, 270¡, 450¡, etc., and equivalent for radian mode. • For SIN or COS : x > 1. • For nCr or nPr: n or r are not integers  0. • For x!: x is not an integer between 0 and 69. EQUATION LENGTH ERROR —...

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• You press < on a blank equation or an equation with only numbers. Invalid Data Type — In an editor, you entered a type that is not allowed, such as a complex number, matrix, or vector, as an element in the stat list editor, matrix editor and vector editor.

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STAT — You attempted to calculate 1var or 2var stats with no defined data points, or attempted to calculate 2var stats when the data lists are not of equal length. SYNTAX — The command contains a syntax error: entering more than 23 pending operations or 8 pending values; or having misplaced functions, arguments, parentheses, or commas.

Page 76: Battery Information
Discard used batteries according to local regulations. How to remove or replace the battery The TI36X Pro calculator uses one 3 volt CR2032 lithium battery. Remove the protective cover and turn the calculator face downwards.

Page 77: In Case Of Difficulty
Dispose of the dead battery immediately and in accordance with local regulations. Per CA Regulation 22 CCR 67384.4, the following applies to the button cell battery in this 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.

Page 78: Texas Instruments Support And Service
Customers in the U.S., Canada, Mexico, Puerto Rico and Virgin Islands: Always contact Texas Instruments Customer Support before returning a product for service. All other customers: Refer to the leaflet enclosed with this product (hardware) or contact your local Texas Instruments retailer/distributor.
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