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HP 32sii Calculator - Trigonometry

Introduction
This document pertains to trigonometric functions for the HP32sii Calculator.
Calculator symbol key
The procedures in this document use the following text to represent symbol keys:
Key
Description
Text Representation
Right shift key
RS
Left-shift key
LS
pi
pi
Entering pi
Press RS, then pi to place the first 12 digits of pi into the X-register. (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 12-digit 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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