# What is the inverse cosine of sqrt2/2?

Oct 24, 2015

$\arccos \left(\frac{\sqrt{2}}{2}\right) = \frac{\pi}{4}$

#### Explanation:

"inverse cos" may also be written as ${\cos}^{- 1}$ or "arccos"

If $\arccos \left(\frac{\sqrt{2}}{2}\right) = \theta$

$\Rightarrow \textcolor{w h i t e}{\text{XXX}} \cos \left(\theta\right) = \frac{\sqrt{2}}{2}$

This is a standard ratio for the angle $\theta = \frac{\pi}{4}$

Note: the inverse cosine is defined as having values restricted to the range $\left[0 , \pi\right)$ and therefore $\frac{\pi}{4}$ is the only valid solution.