Question

How do you simplify `sin^-1 (sin ((2pi)/3))`?

Answer 1

The inverse sine is multivalued, so we need to include `{2pi}/3,` its supplement which shares a sine, and all coterminal angles:

`arcsin sin({2pi}/3) = {2pi}/3 + 2pi k or pi/3 + 2pi k quad` integer `k`

The principal value is `pi/3`