# How do you evaluate cot^-1(1/sqrt3) without a calculator?

May 16, 2017

$\text{arc} \cot \left(\frac{1}{\sqrt{3}}\right) = \frac{1}{3} \pi$

#### Explanation:

Let $\theta = \text{arc} \cot \left(\frac{1}{\sqrt{3}}\right)$

$\cot \theta = \frac{1}{\sqrt{3}}$

$\tan \theta = \sqrt{3}$

This is one of the angles you should know and works out to be $\frac{1}{3} \pi$