Answer
$-\frac{\pi}{2}.$
Work Step by Step
We know that if $\sin y=x$, then $\sin^{-1}(x)=y.$
The domain of $\sin^{-1}{x}$ is the range of $\sin{x}$, which is $[−1, 1] $.
The range of $\sin^{-1}{x}$ is a specified domain of $\sin{x}$, i.e. $\left[− \frac{\pi}{2} , \frac{\pi}{2} \right]$.
We know that $\sin(-\frac{\pi}{2})=-1$, hence $\sin^{-1}(-1)=-\frac{\pi}{2}.$
