Answer
$cos^{-1}\big(cos(\frac{7\pi}{6})\big) = \frac{5\pi}{6}$
Work Step by Step
We can first evaluate $cos(\frac{7\pi}{6})$, which is equal to $-\frac{\sqrt{3}}{2}$. From there, we can evaluate $cos^{-1}\big(-\frac{\sqrt{3}}{2}\big) = \frac{5\pi}{6}$. Note that the range of $cos^{-1}(x)$ is limited to $[0, \pi]$, so even though $cos(\frac{7\pi}{6}) = -\frac{\sqrt{3}}{2}$, $\frac{7\pi}{6}$ is not in the range of inverse cosine.
