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

Oct 6, 2016

$\left\{- \frac{\pi}{3} , - \frac{2 \pi}{3}\right\} + 2 \pi \cdot \mathbb{Z}$

#### Explanation:

${\sin}^{-} 1 \left(- \frac{\sqrt{3}}{2}\right) = x$

$- \frac{\sqrt{3}}{2} = \sin x$

x_1 = -60º or x_2 = - 180º + 60º

if ${x}_{i}$ is a solution, then ${x}_{i} + 2 k \pi$ are also solutions. $k \in \mathbb{Z}$

$- \frac{\pi}{3} + 2 k \pi$ or $- \pi + \frac{\pi}{3} + 2 k \pi$