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

May 23, 2016

${\cos}^{- 1} \left(\frac{1}{2}\right) = 2 n \pi \pm \frac{\pi}{3}$ where $n$ is an integer.

#### Explanation:

We know that $\cos \left(\frac{\pi}{3}\right) = \frac{1}{2}$, however as

$\cos \left(- \theta\right) = \cos \theta$, we also have $\cos \left(- \frac{\pi}{3}\right) = \frac{1}{2}$

Further function cosine has a periodicity of $2 \pi$

hence ${\cos}^{- 1} \left(\frac{1}{2}\right) = 2 n \pi \pm \frac{\pi}{3}$ where $n$ is an integer.