# How do you do simplify csc^-1 (-(2sqrt3)/3)?

$- \frac{\pi}{3} , - \frac{2 \pi}{3}$
$\csc x = \frac{1}{\sin} x$
$\csc x = \left(\frac{- 2 \sqrt{3}}{3}\right)$ --> $\sin x = \left(- \frac{3}{2 \sqrt{3}}\right) = - \frac{\sqrt{3}}{2}$
$\sin x = - \frac{\sqrt{3}}{2}$ --> arc $x = - \frac{\pi}{3}$ and $x = - \frac{2 \pi}{3}$.