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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.
To set an angular mode, press LS, then MODES. A menu will display from which an option can be selected.
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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