# How do you solve and find the value of sin(arctan(sqrt3/3))?

Mar 19, 2018

color(red)(theta = n pi + pi/6 color(white)(aaa) color(green)(n in ZZ

#### Explanation:

Let $\theta = \arctan \left(\frac{\sqrt{3}}{3}\right)$

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

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

$\theta = \frac{\pi}{6} = {30}^{\circ}$

Genaralozing,

$\theta = n \pi + \frac{\pi}{6} \textcolor{w h i t e}{a a a}$ $n \in \mathbb{Z}$