# How do you evaluate cos^-1(cos((pi)/10))?

Dec 12, 2016

The answer is $\frac{\pi}{10}$

#### Explanation:

By definition, ${\cos}^{- 1} \left(x\right)$ is an angle $\phi$ that satisfies two requirements:

(1) $\cos \phi = x$ (the main part of a definition)

(2) $0 \le \phi \le \pi$ (to assure uniqueness of the result)

In our case $x = \cos \left(\frac{\pi}{10}\right)$, so the first requirement is $\cos \left(\phi\right) = \cos \left(\frac{\pi}{10}\right)$ and the obvious candidate for $\phi$ is $\frac{\pi}{10}$.

For this $\phi = \frac{\pi}{10}$ the second requirement is held.

Therefore, the answer is $\frac{\pi}{10}$.