Question

How do you evaluate `arcsin(sin3)`?

Answer 1

`arcsin(sin(3))=pi-3`

Explanation:

Note that `arcsin` maps `[-1,1]` to `[-pi/2,pi/2]`.

We need to find an angle `x in [-pi/2,pi/2]` where `sin(x)=sin(3)`.

Since `sin(x)` is symmetric about `x=pi/2` we have `sin(3)=sin(pi-3)`. `pi-3` is in `[-pi/2,pi/2]`, therefore we have:

`arcsin(sin(3))=pi-3`