# What would the inverse function of y=sin x look like?

Jul 11, 2018

#### Explanation:

Given: $y = \sin x$

In order for a function to have an inverse it must pass both the vertical line test and the horizontal line test:

Graph of $\sin x$:
graph{sin x [-6.283, 6.283, -2, 2]}

In order for the $y = \sin x$ function to have an inverse, we need to limit the domain to $\left[- \frac{\pi}{2} , \frac{\pi}{2}\right] \implies \text{range } \left[- 1 , 1\right]$

The inverse function is $y = \arcsin x = {\sin}^{-} 1 x :$
graph{arcsin x [-4, 4, -2, 2]}