Answer
-2 is not part of the domain
Work Step by Step
arc$\sin (-2)=\sin^{-1} (-2)$
Comparing the above expression to $y=\sin^{-1} x$, this means that we need to find $y$ when $x=-2$. Since $-2$ is not part of the domain, this means that arc$\sin (-2)$ is not defined.
