Answer
$\frac{5\pi}{6}$
Work Step by Step
$\cos \frac{7\pi}{6}=\cos(\pi+\frac{\pi}{6})=-\cos \frac{\pi}{6}=-\frac{\sqrt 3}{2}$
Now $-\frac{\sqrt 3}{2}=-\cos\frac{\pi}{6}=\cos (\pi-\frac{\pi}{6})=\cos \frac{5\pi}{6}$
The angle $\frac{5\pi}{6}$ is within the restricted interval ($0\leq\frac{\pi}{6}\leq\pi$). Therefore,
$\cos^{-1}(\cos \frac{7\pi}{6})=\cos^{-1}(-\frac{\sqrt 3}{2})=\frac{5\pi}{6}$
