# Inverse Trigonometric Functions

Definition: There are inverse functions for all six trigonometric functions. The notation for inverse trigonometric functions can be written two ways,
$\dpi{150} \bg_white f(x) = arcsin\;x = sin^{-1}\;x$where f(x) is the angle and x is the value of that particular trigonometric function.

Inverse trigonometric functions are helpful for finding unknown angle measures given two sides of a right triangle.

Example: Find the measure of angle x.Solution:

Step 1: Here we are given the values for the opposite side and hypotenuse, so can use the sine function to express this as sin x = 2/5.

Step 2: Take the inverse sine of both sides to cancel out the sine function. Use a calculator to simplify, rounding to the nearest hundredth.

$\dpi{150} \bg_white \\sin x = 2/5\\\\sin^{-1}(sin\;x) = sin^{-1}(2/5)\\ \\x = sin^{-1}(2/5)\\ \\x = 23.58^{\circ}$

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