## Trigonometry (11th Edition) Clone

$\displaystyle \frac{5\pi}{6}$
Inverse Cosine Function $y=\cos^{-1}x$ or $y=$ arccos $x$ means that $x=\cos y$, for $0 \leq y \leq \pi$. ------------------- 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$(-\displaystyle \frac{\sqrt{3}}{2})=\frac{5\pi}{6}$