How do you evaluate sec^-1(2/sqrt3) without a calculator?

Dec 1, 2016

${\sec}^{- 1} \left(\frac{2}{\sqrt{3}}\right) = \frac{\pi}{6}$

Explanation:

Find $x$ such that $\sec x = \frac{2}{\sqrt{3}}$

As:

$\sec x = \frac{1}{\cos} x$

this is the same as finding $x$ such that $\cos x = \frac{\sqrt{3}}{2}$ and we know that:

$\cos \left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}$