Answer
$\displaystyle \frac{5\pi}{6}$
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 $\displaystyle \cos\frac{\pi}{6}=\frac{\sqrt{3}}{2}.$
Also, $\cos(\pi-x)=-\cos x.$
In the interval $0 \leq y \leq \pi, $we find $y=\displaystyle \pi-\frac{\pi}{6} =\displaystyle \frac{5\pi}{6}$
such that $\displaystyle \cos(\frac{5\pi}{6}) =-\displaystyle \frac{\sqrt{3}}{2}$
so
$y=$ arccos$(-\displaystyle \frac{\sqrt{3}}{2})=\frac{5\pi}{6}$
