Answer
$cos^{-1}(-\frac{1}{2}) = \frac{2\pi}{3}$
Work Step by Step
The domain of $cos^{-1}(x)$ is $[\frac{-\pi}{2}, \frac{\pi}{2}]$ and $x=-\frac{1}{2}$ is in the domain. Since $cos(\frac{2\pi}{3}) = -\frac{1}{2}$, $cos^{-1}(-\frac{1}{2}) = \frac{2\pi}{3}$.
