Answer
$\frac{5\pi}{6}.$
Work Step by Step
The domain of $\cos^{-1}{x}$ is the range of $\cos{x}$, which is $[−1, 1] $.
The range of $\cos^{-1}{x}$ is a specified domain of $\cos{x}$, i.e. $\left[0,\pi \right]$.
We know that if $\cos y=x$, then $\cos^{-1}(x)=y.$
We know that $\cos(\frac{5\pi}{6})=-\frac{\sqrt3}{2}$, hence $\cos^{-1}(-\frac{\sqrt3}{2})=\frac{5\pi}{6}.$
