#### Answer

$\pi$

#### Work Step by Step

$y=\cos^{-1}x$ is the number in $[0, \pi]$ for which $\cos y=x.$
As the value of cosine approaches $-1,$ (from the right, because it can't approach it from the left - cosine is never less than -1) the angle we approach (in radians) is $\pi$.
Alternatively (if in doubt), we can reach the same conclusion by observing the graph of $y=\cos^{-1}x$
(also written as $\arccos x$) in the vicinity of $x=-1$. See below.