How do you find the inverse of sin?

1 Answer
Apr 15, 2015

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.