Texas Instruments TI-36X Pro User Manual

1

TI-36X 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

Multi-tap keys......................................................................... 8

Menus.................................................................................... 8

Scrolling expressions and history .......................................... 9

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

Rectangular to polar ............................................................ 23

Trigonometry........................................................................ 24

Hyperbolics .......................................................................... 26

Logarithm and exponential functions................................... 27

Numeric derivative............................................................... 27

Numeric integral................................................................... 29

Stored operations ................................................................ 30

Memory and stored variables .............................................. 31

Data editor and list formulas ................................................ 34

2

Statistics, regressions, and distributions.............................. 36

Probability............................................................................ 48

Function table ...................................................................... 49

Matrices ............................................................................... 52

Vectors................................................................................. 54

Solvers................................................................................. 56

Number bases ..................................................................... 61

Expression evaluation.......................................................... 63

Constants............................................................................. 64

Conversions......................................................................... 66

Complex numbers................................................................ 69

Errors................................................................................... 71

Battery information............................................................... 76

In case of difficulty ............................................................... 77

Texas Instruments Support and Service.............................. 78

Important information

Texas Instruments makes no warranty, either express or
implied, including but not limited to any implied warranties of
merchantability and fitness for a particular purpose, regarding
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 damages in connection with or
arising out of the purchase or use of these materials, and the
sole and exclusive liability of Texas Instruments, regardless of
the form of action, shall not exceed the purchase price of this
product. Moreover, Texas Instruments shall not be liable for
any claim of any kind whatsoever against the use of these
materials by any other party.

MathPrint, APD, Automatic Power Down and EOS are
trademarks of Texas Instruments Incorporated.

Copyright © 2010 Texas Instruments Incorporated

3

Examples

Each section is followed by instructions for keystroke
examples that demonstrate the TI-36X Pro functions.

Examples assume all default settings, as shown in the Modes
section.

Some screen elements may differ from those shown in this
document.

Switching the calculator on and off

& turns on the calculator. % ' turns it off. The display
is cleared, but the history, settings, and memory are retained.

The APD™ (Automatic Power Down™) feature turns off the
calculator automatically if no key is pressed for about 5
minutes. Press & after APD. The display, pending
operations, settings, and memory are retained.

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 the screen) or U (to lighten the

screen).

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 TI-36X 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
view the entire entry or expression.

In the MathPrint™ mode, you can enter up to four levels of
consecutive nested functions and expressions, which include

fractions, square roots, exponents with ^, Ü, e

x

, and 10x.

4

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.

Indicator Definition

2ND 2nd function.
FIX Fixed-decimal setting. (See Mode

section.)

SCI, ENG Scientific or engineering notation.

(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
displayed for default DEC mode.

The calculator is performing an
operation.

5 6 An entry is stored in memory before

and/or after the active screen. Press

# and $ to scroll.

³´ An entry or menu displays beyond

16 digits. Press ! or " to scroll.
Normal cursor. Shows where the

next item you type will appear.
Entry-limit cursor. No additional

characters can be entered.
Placeholder box for empty

MathPrint™ element. Use arrow
keys to move into the box.

5

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. Press % to activate the secondary
function of a given key. Notice that 2ND appears as an
indicator on the screen. To cancel it before entering data,
press % again. For example, %b 25 < calculates
the square root of 25 and returns the result, 5.

Modes

q

Use q to choose modes. Press $ # ! " to choose 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 angle mode to degrees,
radians, or gradians.

NORM SCI ENG Sets the numeric notation mode.
Numeric notation modes affect only the display of results, and
not the accuracy of the values stored in the unit, which remain
maximal.

NORM displays results with digits to the left and right of the
decimal, as in 123456.78.

MathPrint™ cursor. Continue
entering the current MathPrint™
element, or press an arrow key to
exit the element.

Indicator Definition

6

SCI expresses numbers with one digit to the left of the
decimal and the appropriate power of 10, as in

1.2345678

E5 (which is the same as 1.2345678×10

5

).

ENG displays results as a number from 1 to 999 times 10
to an integer power. The integer power is always a multiple
of 3.

Note: E is a shortcut key to enter a number in scientific
notation format. The result displays in the numeric notation
format selected in the mode menu.

FLOAT 0 1 2 3 4 5 6 7 8 9 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 display to the right of the
decimal.

REAL a+bi r±q Sets the format of complex number
results.

REAL real results
a+bi rectangular results
r±q polar results

DEC HEX BIN OCT Sets the number base used for

calculations.

DEC decimal
HEX hexadecimal (To enter hex digits A through F, use

%§, %¨, and so on.)

BIN binary
OCT octal

CLASSIC MATHPRINT

CLASSIC mode displays inputs and outputs in a single

line.
MATHPRINT mode displays most inputs and outputs in

textbook format.

7

Examples of Classic and MathPrint™ modes

Classic 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 root example

Cube root example Cube root example

8

Multi-tap keys

A multi-tap 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.
Multi-tap keys include z, X, Y, Z, C, D,

H, and g. Applicable 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 multiple menus.

Press " and $ to scroll and select a menu item, or press
the corresponding number next to the item. To return to the
previous screen without selecting the item, press -. To
exit a menu and return to the Home screen, press %s.

%h (key with a single menu):

RECALL VAR (with values set to default of 0)
1: x = 0
2: y = 0
3: z = 0
4: t = 0
5: a = 0
6: b = 0
7: c = 0
8: d = 0

9

d (key with multiple menus):

Scrolling expressions and history

! " # $
Press ! or " to move the cursor within an expression that

you are entering or editing. Press %! or % " to move
the cursor directly to the beginning or end of the expression.

After you evaluate an 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 you
can edit it and evaluate a new expression.

Example

MATH NUM DMS R ³´ P

1:4

n

/d³´Un/

d

1: abs( 1: ¡ 1: P ´Rx(

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( 5: g
6: prod( 6: min( 6: ´DMS

7: max(
8: mod(

Scroll 7 F U 4

(3 )(1 ) <

%b ## <
<

r

10

Answer toggle

r

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.

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 calculator is turned off. To recall the value of ans:

•Press %i (ans displays on the screen), or

• Press any operations key (T, U, and so forth) as the first

part of an entry. ans and the operator are both displayed.

Examples

Answer
toggle

%b 8 <

r

ans 3 V 3 <

V 3 <

11

Order of operations

The TI-36X 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.

3 %c %i
<

1st Expressions inside parentheses.
2nd Functions that need a ) and precede the

argument, such as sin, log, and all R³´P menu

items.
3rd Fractions.
4th Functions that are entered after the argument,

such as x

2

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 2^3^2 is evaluated as (2^3)^2, with

a result of 64.

In MathPrint™ mode, exponentiation using the

G key is evaluated from right to left. The

expression 2^3^2 is evaluated as 2^(3^2), with

a result of 512.

The calculator evaluates expressions entered

with F and a from left to right in both Classic

and MathPrint™ modes. Pressing 3 F F is

calculated as (3

2)2

=81.

6th

Negation (

M).

12

Examples

7th Permutations (nPr) and combinations (nCr).
8th Multiplication, implied multiplication, division.
9th Addition and subtraction.
10th Conversions (n/d³´Un/d, F³´D, 4DMS).
11th < completes all operations and closes all

open parentheses.

+ Q P M 6 0 T 5 V M1 2 <

(M) 1 T M 8 T 1 2 <

%b 9 T 16 <

( ) 4 V ( 2 T 3 ) <

4 ( 2 T 3 ) <

^ and ‡ %b 3 G 2 " T 4

G 2 <

13

Clearing and correcting

Fractions

P%@d 1 %˜

In the MathPrint™ mode, fractions with P can include real
and complex numbers, operation keys (T, V, etc.), and
most function keys (F, % _, etc.).

In Classic mode, fractions with P do not allow operation
keys, functions, or complex fractions in the numerator or
denominator.

Note: In Classic mode, only number entries are supported
when using P. Fractions in Classic mode are shown with a
double-thick fraction bar (for example, ). The numerator
must be an integer, and the denominator 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 automatically simplified.

%s 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.

J Deletes the character at the cursor.
%f Inserts a character at the cursor.
%{ Clears variables x, y, z, t, a, b, c, and d

to their default value of 0.

% 2 Resets the calculator. Returns unit to

default settings; clears memory
variables, pending operations, all
entries in history, and statistical data;
clears any stored operation, and ans.

14

• 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).

• In MathPrint™ mode, press $ between the entry of the

numerator and the denominator.

• In Classic mode, press P between the entry of the

numerator and the denominator. The fraction bar will
appear thicker than the division bar.

• Pressing % # from any MathPrint™ level, including the

denominator or a lower 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, press %# to scroll to the
desired entry, and then press < to paste the entry to
the denominator.

– To paste a previous entry in the numerator or unit, place

the cursor in the numerator or unit, press # or %#
to scroll to the desired entry, and then press < to
paste the entry to the numerator or unit.

• % @ enters a mixed number. Press the arrow keys to

cycle through the unit, numerator, and denominator.

• d 1 converts between simple fractions and mixed-

number form (4

n

/d³´Un/d).

• %˜ converts results between fractions and

decimals.

Examples Classic mode

n

/d, Un/

d

3 P 4 T 1 % @ 7
P 12 <

n

/d ³´Un/

d

9 P 2 d 1 <

15

Examples MathPrint™ mode

Percentages

%_

To perform a calculation involving a percentage, press
%_ after entering the value of the percentage.

Example

F³´D 4 % @ 1 P 2

%˜ <

n/d, U n/d P3 $ 4 " T 1

% @ 7 $12 <

n

/d ³´Un/

d

9 P 2 " d 1 <

F³´D 4 % @ 1 $ 2 "

%˜ <

Examples
(MathPrint™
mode only)

P1.2 T 1.3 $ 4 <

(MathPrint™
mode only)

P M 5 T %b 5
F U 4 ( 1 ) ( 6
) $ 2 ( 1 ) <

2 %_ V 150 <

16

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?

The two extractions represent a total of 317.9 tons of metal for
a total value of 89012 dollars.

EE key

E
E is a shortcut key to enter a number in scientific notation

format.

Example

3 %_ V 5000 <

T 2.3 %_ V 7300 <

V 280 <

2 E 5 <

q $ " <

- <

17

Powers, roots and inverses

Examples

F Calculates the square of a value. The

TI-36X Pro calculator evaluates expressions
entered with F and a from left to right in
both Classic and MathPrint™ modes.

G Raises a value 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 negative
value.

a Gives the inverse of a value: 1/x. The calculator

evaluates expressions entered with F and a
from left to right in both Classic and
MathPrint™ modes.

q$<­5 F T 4 G 2 T 1 "
<

10 G M 2 <

%b 49 <

%b 3 F T 2 G 4 <

6 %c 64 <

18

Pi

g (multi-tap key)

p = 3.141592653590 for calculations.
p = 3.141592654 for display.

Example

³ Problem

What is the area of a circle if the radius is 12 cm?

Reminder: A = p×r

2

The area of the circle is 144 p square cm. The area of the
circle is approximately 452.4 square cm when rounded to one
decimal place.

2 %a <

p 2 V g <

r

g V 12 F <
r

19

Math

d MATH
d displays the MATH menu:

Examples

1:4

n

/d³´Un/

d

Converts 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

/d³´Un/

d

9 P 2 " d 1 <

lcm( d 2

6 %` 9 ) <

gcd( d 3

18 %` 33 ) <

4Pfactor 253 d 4 <

sum( d 5

1 " 4 " z V 2
<

prod(Sd 6

1 " 5 " 1 P z

" " <

20

Number functions

d NUM
d " displays the NUM menu:

Examples

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( Maximum of two numbers
8: mod( Modulo (remainder of first number P second

number)

abs( d " 1

M % b 5 <

round( d " 2

1.245 %` 1 ) <
## <
!!!!! 5 <

iPart(
fPart(

4.9 L z <
d "3 z ) <
d "4 z )
V 3 <

int( d "5

M 5.6 ) <

min(
ma

x(

d "6
4 %`M5 ) <
d "7
.6 %` .7 ) <

21

Angles

d DMS
d " " displays the DMS menu:

You can also convert between rectangular coordinate form
(R) and polar coordinate form (P). (See Rectangular to polar
for more information.)

Choose an angle mode from the mode screen. You can
choose from DEG (default), RAD, 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 as degrees (º).
2: ¢ Specifies the angle unit modifier as minutes (').
3: £ Specifies the angle unit modifier as seconds (").
4: r Specifies a radian angle.
5: g Specifies a gradian angle.
6: ´DMS Converts angle from decimal degrees to

degrees, minutes, and seconds.

RAD q"<

­X 30 d""

1 ) <

22

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.

The result is 39 degrees, 26 minutes and 23 seconds.

³ Problem

It is known that 30¡ = p / 6 radians. In the default mode,
degrees, find the sine of 30¡. Then set the calculator to radian
mode and calculate the sine of p / 6 radians.

DEG q<

-
2 g d " " 4
<

4DMSS 1.5 d"" 6 <

-q$$"""<

-12 d""

1
31 d""2
45 d"" 3
T 26 d""1
54 d"" 2
38 d"" 3 <

d"" 6 <

23

Note: Press - to clear the screen between problems.

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.

Rectangular to polar

d R³´P
d! displays the R³´P menu, which has functions for

converting coordinates between rectangular (x,y) 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 polar coordinates. Round the results to one
decimal place.

- X 30 ) <

q " < ­X g P 6 " ) <

X 30 d"" < ) <
q < ­X g P 6 " d"" 4
) <

1: P ´Rx( Converts polar to rectangular and displays x.
2: P ´Ry( Converts polar to rectangular and displays y.
3: R ´Pr( Converts rectangular to polar and displays r.
4: R ´Pq(

Converts rectangular to polar and displays q.

R³´P - q $ $ " "

<

24

Converting (r, q) = (5, 30) gives (x, y) = (4.3, 2.5) and
(x, y) = (3, 4) gives (r, q) = (5.0, 53.1).

Trigonometry

XYZ(multi-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 Radian Mode

- d ! 1
5 %` 30 ) <
d ! 2
5 %` 30 ) <

d !3
3 %` 4 ) <
d ! 4
3 %` 4 ) <

tan q $ $ < -

Z 45 ) <

tan

-1

­ZZ 1 ) <

cos -

5 V Y 60 ) <

tan q " < -

Z g P 4 " )
<