# How do you evaluate \sec^{-1} \sqrt{2} ?

Nov 5, 2014

Let $\theta = {\sec}^{- 1} \sqrt{2}$.

By rewriting in terms of secant,

$\implies \sec \theta = \sqrt{2}$

by taking the reciprocal,

$\implies \cos \theta = \frac{1}{\sqrt{2}}$

$\implies \theta = \frac{\pi}{4}$

I hope that this was helpful.