Question

How do you find the inverse of sin?

Answer 1

The inverse of the `sin` function is the `arcsin` function.
But sine itself, would not be invertible because it's not injective, so it's not bijective (invertible).
To obtain arcsine function we have to restrict the domain of sine to `[-pi/2,pi/2]`.

`arcsin(sin(theta)) = theta " if and only if"-pi/2<=theta<=pi/2`

For example:
Since `sin(pi/6) = 1/2`
`arcsin(1/2) = pi/6`

If you meant by your question "how do you calculate the value of the `arcsin` for some given number?"
then the answer is that there is no easy way to do this (with the exception of a few special values) just as there is no easy way to calculate the value of `sin` for most values.