# What is the Inverse cosine of (-rad3/2)?

Jan 9, 2016

${\cos}^{-} 1 \left(- \frac{\sqrt{3}}{2}\right) = \frac{5 \pi}{6}$

#### Explanation:

${\cos}^{-} 1 \left(- \frac{\sqrt{3}}{2}\right)$

The range of ${\cos}^{-} 1 \left(x\right)$ is $\left[0 , \pi\right]$

$\cos \left(\theta\right) = - \frac{\sqrt{3}}{2}$ at $\theta = \frac{5 \pi}{6}$

Therefore, ${\cos}^{-} 1 \left(- \frac{\sqrt{3}}{2}\right) = \frac{5 \pi}{6}$