# What is the inverse of cosine (-1/2)?

Sep 7, 2015

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

#### Explanation:

The inverse cos function (${\cos}^{- 1}$) is restricted to a range of $\left[0 , \pi\right]$

If $\theta = s o {c}^{- 1} \left(- \frac{1}{2}\right)$
then
$\textcolor{w h i t e}{\text{XXXX}} \cos \left(\theta\right) = - \frac{1}{2}$

The only angle within the range $\left[0 , \pi\right]$ that satisfies this condition is pictured below: