# How do you find the exact value for tan 120?

Mar 17, 2018

color(indigo)(tan 120 = -sqrt3

#### Explanation:

$\hat{120} = \hat{\frac{120}{180}} = \frac{\hat{2 \pi}}{3}$

Angle falls in II Quadrant and $\tan$ is negative.

$\therefore \tan 120 = \tan \left(\frac{2 \pi}{3}\right) = \tan \left(\frac{2 \pi}{3} - \pi\right) = - \tan \left(\frac{\pi}{3}\right)$

$- \tan \left(\frac{\pi}{3}\right) = - \sqrt{3}$