# How do you solve Cos theta Tan theta+sqrt(3)Cos theta=0 for [0,2pi]?

Sep 26, 2015

$\theta = \frac{5 \pi}{6}$ and $\frac{11 \pi}{6}$

#### Explanation:

$\cos \theta \cdot \left(\sin \frac{\theta}{\cos} \theta\right) + \sqrt{3} \cos \theta = 0$

You know that $\tan \theta = \sin \frac{\theta}{\cos} \theta$, which means that you have

$\sin \theta + \sqrt{3} \cos \theta = 0$

$\sin \theta = - \sqrt{3} \cdot \cos \theta$

$\tan \theta = - \sqrt{3}$ for $\left[0 , 2 \pi\right]$,

$\theta = \pi - \left(\frac{\pi}{3}\right)$ and $2 \pi - \left(\frac{\pi}{3}\right)$

$\theta = \frac{5 \pi}{6}$ and $\frac{11 \pi}{6}$