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

Aug 29, 2016

$\frac{\pi}{10}$

#### Explanation:

Given a function $f \left(x\right)$ and its inverse ${f}^{-} 1 \left(x\right)$

Then ${f}^{-} 1 \left(f \left(x\right)\right) = x$

$\therefore {\sec}^{-} 1 \left(\sec \left(- \frac{\pi}{10}\right)\right) = \left\mid \frac{\pi}{10} \right\mid$

However, since the range of ${\sec}^{- 1} \left(x\right)$ is $\left[0 , \frac{\pi}{2}\right) \cup \left(\frac{\pi}{2} , \pi\right]$

$x = \frac{\pi}{10}$