#### Answer

$\cos^{-1}(-2)$ does not exist.

#### Work Step by Step

Solve for radians, then convert to degrees.
$y=\cos^{-1}x$
Domain:$[-1, 1] $
Range: $[0, \pi]$
Quadrants (unit circle): I and II
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$y$ is the number from $[0, \pi]$
such that $\cos y=-2.$
But,
such a y does not exist,
as cosine can not be less than $-1$.
More directly,
$-2$ is not in the domain of $\cos^{-1}x$, so
$\cos^{-1}(-2)$ does not exist.