# How do you calculate tan^-1(sqrt3)?

Apr 25, 2015

Assuming by ${\tan}^{- 1} \left(\sqrt{3}\right)$you mean $\arctan \left(\sqrt{3}\right)$

and not 1/(tan(sqrt(3))

We are looking for a value $\theta$
such that
$\tan \left(\theta\right) = \sqrt{3}$
that is
$\theta = \arctan \left(\tan \left(\theta\right)\right) = \arctan \left(\sqrt{3}\right)$

$\tan \left(\theta\right) = \sqrt{3}$
is the $\tan$ of a standard triangle
with $\theta = \frac{\pi}{3}$

That is $\arctan \left(\sqrt{3}\right) = P \frac{I}{3}$