# How do you calculate the cos^-1 (-1/2)?

Nov 21, 2015

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

#### Explanation:

If ${\cos}^{- 1} \left(- \frac{1}{2}\right) = \theta$
then
$\textcolor{w h i t e}{\text{XXX}} \cos \left(\theta\right) = - \frac{1}{2}$
with a further restriction $0 \le {\cos}^{- 1} \le \pi$

From the above diagram, we can see
$\textcolor{w h i t e}{\text{XXX}} \theta = \frac{2 \pi}{3}$