# How do I find the value of tan 5pi / 6?

$- \frac{\sqrt{3}}{3}$
$\tan \left(\frac{5 \pi}{6}\right) = \tan \left(\pi - \frac{\pi}{6}\right) = \frac{\tan \pi - \tan \left(\frac{\pi}{6}\right)}{1 + \tan \left(\pi\right) \tan \left(\frac{\pi}{6}\right)} = - \tan \left(\frac{\pi}{6}\right) = - \frac{1}{\sqrt{3}} = - \frac{\sqrt{3}}{3}$