# How do you evaluate arctan((1/sqrt3)?

Jul 22, 2015

$\arctan \left(\frac{1}{\sqrt{3}}\right) = \frac{\pi}{6} \mathmr{and} {30}^{o}$

#### Explanation:

This ratio is one of the standard trigonometric triangles:

$\arctan$ must provide an angle in quadrants one or four; in quadrant four, the argument would have needed to be negative.

The ratio $\frac{\left(\frac{1}{2}\right)}{\left(\frac{\sqrt{3}}{2}\right)} = \frac{1}{\sqrt{3}}$
$\textcolor{w h i t e}{\text{XXXX}}$is that of a $\frac{\pi}{6}$ angle (as indicated above).