This document pertains to trigonometric functions for the HP32sii Calculator.
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HP 32sii Calculator  Trigonometry
Calculator symbol key
The procedures in this document use the following text to represent symbol keys:
Key

Description

Text Representation


Right shift key

RS


Leftshift key

LS


pi

pi

Entering pi
Press RS, then pi to place the first 12 digits of pi into the Xregister. (The number displayed depends on the display format.) Because pi is a function, it does not need to be separated from another number by ENTER.
note:
A calculator cannot exactly represent pi, since pi is an irrational number.
Setting the angular mode
The angular mode specifies which unit of measure to assume for angles used in trigonometric functions. The mode does not convert numbers already present.
360 degrees = 2pi radians = 400 grads
To set an angular mode, press LS, then MODES. A menu will display from which an option can be selected.
Option

Display

Description

DG

Sets Degrees mode (DEG). Uses decimal degrees, not degrees, minutes, and seconds.


RD

RAD

Sets Radians mode (RAD).

GR

GRAD

Sets Grads mode (GRAD).

Trigonometric functions
With x in the display:
Press::

To Calculate:

SIN

Sine of x

COS

Cosine of x

TAN

Tangent of x

LS, then ASIN

Arc sine of x

LS, then ACOS

Arc cosine of x

LS, then ATAN

Arc tangent of x

note:
Calculations with the irrational number pi cannot be expressed exactly by the 12digit internal precision of the calculator. This is particularly noticeable in trigonometry. For example, the calculated sin pi (radians) is not zero, but 2.0676 x 10 ^{13}, a very small number close to zero.
Example of trigonometric function
Show that the cosine (5/7) pi radians and cosine 128.57 degrees are equal (to four significant digits).
Keys

Display

Description

Press LS, MODES, then RD

Sets Radians mode; RAD annunciator on.


Press [.], 5, [.], 7, then ENTER

0.7143

5/7 in decimal format.

Press RS, pi, x, then COS

0.6235

Cos (5/7)pi

Press LS, MODES, then DG

0.6235

Switches to Degrees mode (no annunciator).

Press 1, 2, 8, [.], 5, 7, then COS

0.6235

Calculates cos 128.57 degrees, which is the same as cos (5/7)pi.

Programming note
Equations using inverse trigonometric functions to determine an angle often look like Figure 1.
Figure : Formula for determining angle
If x = 0, then y/x is undefined, resulting in the error "DIVIDE BY 0". For a program, then, it would be more reliable to determine by a rectangular to polar conversion, which converts (x, y) to (r, angle).
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