Answer
$\frac{2\pi}{3}$
Work Step by Step
The range of $\cos^{-1} x$ is $0\leq\cos^{-1}x\leq\pi$.
We need to find the angle between 0 and $\pi$ whose cosine is $-\frac{1}{2}$.
Knowing that $\cos \frac{\pi}{3}=\frac{1}{2}$ and
$\cos(\pi-x)=-\cos x$, we can write
$-\frac{1}{2}=\cos(\pi-\frac{\pi}{3})=\cos \frac{2\pi}{3}$
Or $\cos^{-1}(-\frac{1}{2})=\frac{2\pi}{3}$
