Question

How do you find the exact value of `sin^-1(-sqrt3/2)`?

Answer 1

`{- pi / 3, - (2 pi) / 3} + 2 pi cdot ZZ`

Explanation:

`sin^-1 (-sqrt 3 / 2) = x`

`-sqrt 3 / 2 = sin x`

`x_1 = -60º or x_2 = - 180º + 60º`

if `x_i` is a solution, then `x_i + 2 k pi` are also solutions. `k in ZZ`

`- pi / 3 + 2 k pi` or `- pi + pi / 3 + 2 k pi`