# How do you find the value of tan^-1 sqrt(3)?

Oct 24, 2015

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

#### Explanation:

Note ${\tan}^{- 1}$ is defined as a function with values restricted to the range $\left[0 , \frac{\pi}{2}\right)$
and
if $\theta = {\tan}^{- 1} \left(\sqrt{3}\right)$
then $\tan \left(\theta\right) = \sqrt{3}$

A basic reference triangle looks like:

$\theta = {60}^{\circ} = \frac{\pi}{3}$