Question

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

Answer 1

See answer below

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 `[-pi/2, pi/2] => "range " [-1, 1]`

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