Question

How do you evaluate `arcsin(sin 2)`?

Answer 1

The range of arcsin is `-pi/2 <= theta <= pi/2`.

`2 > pi/2` so it lies outside the range.

Use `sin (pi-theta) = sin theta`

Then `sin2 = sin (pi-2)`.

`pi-2 ~= 1.14` so `0 < pi-2 < pi/2`

So `arcsin(sin(2)) = pi-2`