The inverse trigonometric functions are the inverse functions of the trigonometric functions. For example, the inverse sine is the inverse function of the sine function. The main inverse trigonometric functions are shown in the table below.

Trigonometric Function	Inverse Trigonometric Function
$f(x)=\sin x$	$f^{\text{-}1}(x)={\sin }^{\text{-}1}x$
$f(x)=\cos x$	$f^{\text{-}1}(x)={\cos }^{\text{-}1}x$
$f(x)=\tan x$	$f^{\text{-}1}(x)={\tan }^{\text{-}1}x$

The inverse trigonometric functions relate an input, which represents the ratio of two sides of a right triangle, to the measure of one of its two acute angles. The output angles are measured in radians. The domain of the corresponding trigonometric function must be restricted in order for its inverse to be defined as a function. The properties of the main inverse trigonometric functions are summarized in the following table.

Inverse Trigonometric Function	Domain	Range
$y={\sin }^{\text{-}1}x$	$[\text{-}1,1]$	$\text{-}\frac{\pi }{2}\le x\le \frac{\pi }{2}$
$y={\cos }^{\text{-}1}x$	$[\text{-}1,1]$	$0\le x\le \pi$
$y={\tan }^{\text{-}1}x$	All real numbers	$\text{-}\frac{\pi }{2}\le x\le \frac{\pi }{2}$

Note that the inverse trigonometric functions ${\sin }^{\text{-}1}x,$ ${\cos }^{\text{-}1}x,$ ${\tan }^{\text{-}1}x$ are also called $\arcsin x,$ $\arccos x,$ and $\arctan x,$ respectively. These can also be written as $\mathrm{A}\mathrm{r}\mathrm{c}\mathrm{s}\mathrm{i}\mathrm{n}x,$ $\mathrm{A}\mathrm{r}\mathrm{c}\mathrm{c}\mathrm{o}\mathrm{s}x,$ and $\mathrm{A}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}x,$ respectively.