Saturday, January 31, 2009

Trigonometric Arcfunctions

Arcfunctions, or inverse functions, of trigonometry allow you to find the degree of an angle if you have the ratios.

Thus arcsin(1/2) = 30 degrees
since sin(30) = 1/2

this can also be written as

sin-1(1/2) = 30 degrees

The arc functions can produce more than one value, for example

arcsin(sqrt2/2) can equal 90 degrees and 135 degrees.

As we learned when we covered functions in set theory, functions can be defined on any domain, and thus, the arc functions are defined to be between -90 and 90 degrees to avoid getting more than one output. That is -Pi/2 and Pi/2 radians.

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