## Precalculus (10th Edition)

$\dfrac{5\pi}{6}$
We know that if $\cos{(y)}=x$, then $\cos^{-1}{x}=y.$ Hence, if $\cos{(\frac{5\pi}{6})}=-\frac{\sqrt3}{2}$, then by the definition of the inverse function: $\cos^{-1}(-\frac{\sqrt3}{2})=\frac{5\pi}{6}$. (because it is in the right domain, in $[0,\pi$)