# How do you find the value of tan 150?

Oct 17, 2015

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

#### Explanation:

$\tan \left(150\right) = \tan \left(180 - 30\right)$

or

$\tan \left(150\right) = \tan \left(180 + \left(- 30\right)\right)$

$\tan \left(150\right) = \frac{\tan \left(180\right) + \tan \left(- 30\right)}{1 - \tan \left(180. \tan \left(- 30\right)\right)}$

$\tan \left(150\right) = \frac{0 + \sin \frac{- 30}{\cos} \left(- 30\right)}{1 - 0}$

$\tan \left(150\right) = \frac{\frac{1}{2}}{- \frac{\sqrt{3}}{2}}$

$\tan \left(150\right) = \left(\frac{1}{2}\right) \cdot \left(\frac{2}{-} \sqrt{3}\right)$

$\tan \left(150\right) = \frac{1}{-} \sqrt{3}$