# How do you find the exact value of cos^-1(cos(pi/7))?

##### 1 Answer
Feb 2, 2017

${\cos}^{- 1} \left(\cos \left(\frac{\pi}{7}\right)\right) = \frac{\pi}{7}$

#### Explanation:

As per definition of ${\cos}^{- 1}$, if $\cos a = x$, $a = {\cos}^{- 1} x$

In the given problem, let $\cos \left(\frac{\pi}{7}\right) = v$

then as per definition ${\cos}^{- 1} v = \frac{\pi}{7}$ .................(1)

and putting value of $v = \cos \left(\frac{\pi}{7}\right)$ in (1), we get

${\cos}^{- 1} \left(\cos \left(\frac{\pi}{7}\right)\right) = \frac{\pi}{7}$