#### Answer

The right side of the equation $\sin^{-1}{x} = \cos^{-1}{(-2)}$ is undefined so the equation does not have a solution. This is because in $\cos^{-1}{(x)}$, $x$ can only be a number from $-1$ to $1$.

#### Work Step by Step

RECALL:
The value of $x$ in $\cos^{-1}{x}$ can only be a real number in the interval $[-1, 1]$.
Thus, the right side of the equation $\sin^{-1}{x} = \cos^{-1}{(-2)}$ is undefined so the equation does not have a solution.