# How do you find the exact value of csc^-1(-1)?

${\csc}^{- 1} \left(- 1\right) = - \frac{\pi}{2}$
${\csc}^{- 1} \left(- 1\right)$ is the angle whose cosecant ratio is $- 1$, i.e. whose sine ratio is $- 1$.
As $\sin \left(- \frac{\pi}{2}\right) = - 1$, hence
${\csc}^{- 1} \left(- 1\right) = - \frac{\pi}{2}$