High School Trigonometry/General Definitions of Inverse Trigonometric Functions

General Definitions of Inverse Trig Functions

Ordinary trigonometric functions yield a value after inputting an angle(1). Inverse trigonometric functions yield an angle after inputting a value(2).

1:$\sin(\theta )=x$

2:$\arcsin(x)=\theta$

As seen above, the notation for the inverse of a trigonometric function is to simply put the letters arc in front of the function name. Sometimes, just an a is used: asin. It may also be represented by a superscripted -1 over the function. For example, sin^-1(x)

Inverse functions exist for all 6 trigonometric functions.

This material was adapted from the original CK-12 book that can be found here. This work is licensed under the Creative Commons Attribution-Share Alike 3.0 United States License