How do you find the exact value of arctan(sqrt3/3)?

Jun 28, 2015

$\arctan \left(\frac{\sqrt{3}}{3}\right) = {30}^{o} = \frac{\pi}{6} r a \mathrm{di} a n s$

Explanation:

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

If $\arctan \left(\frac{1}{\sqrt{3}}\right) = \theta$
$\textcolor{w h i t e}{\text{XXXX}}$then $\tan \left(\theta\right) = \frac{1}{\sqrt{3}}$

$\tan \left(\theta\right) = \frac{1}{\sqrt{3}}$ is indicative of a standard triangle with
$\textcolor{w h i t e}{\text{XXXX}}$$\theta = {30}^{o}$