Answer
$\displaystyle \frac{2\pi}{3}$
Work Step by Step
Inverse Cosine Function
$y=\cos^{-1}x$ or $y=$ arccos $x$ means that
$x=\cos y$, for $ 0 \leq y \leq \pi$.
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In quadrant I, we know: $\ \ \displaystyle \cos\frac{\pi}{3}=\frac{1}{2}.$
Also, $\cos(\pi-x)=-\cos x.$
In the interval $0 \leq y \leq \pi, $we find $y=\displaystyle \pi-\frac{\pi}{3} =\displaystyle \frac{2\pi}{3}$
such that $\displaystyle \cos(\frac{2\pi}{3}) =-\displaystyle \frac{1}{2}$
so
$y=$ arccos$(-\displaystyle \frac{1}{2})=\frac{2\pi}{3}$
