Answer
$-\dfrac{\pi}{2}$
Work Step by Step
$\csc^{-1}{(-1)}=-\dfrac{\pi}{2}$, because $\csc{\left(-\dfrac{\pi}{2}\right)}=-1$ and $-\dfrac{\pi}{2}$ is in the range of $\csc^{-1}{x}$, which is $\left[-\dfrac{\pi}{2}, 0\right) \cup \left(0, \dfrac{\pi}{2}\right].$
