# How do you find the exact value of cos^-1 (-sqrt3/2)?

${\cos}^{- 1} \left(- \frac{\sqrt{3}}{2}\right) = \pm \frac{5 \pi}{6}$
As $\cos \left(\frac{5 \pi}{6}\right) = - \frac{\sqrt{3}}{2}$ and also $\cos \left(- \frac{5 \pi}{6}\right) = - \frac{\sqrt{3}}{2}$. Hence
${\cos}^{- 1} \left(- \frac{\sqrt{3}}{2}\right) = \pm \frac{5 \pi}{6}$