# How do you solve 2costheta+1=0?

##### 1 Answer
Jul 12, 2018

The general solution of $2 \cos \theta + 1 = 0$ is :

$\theta = 2 k \pi \pm \frac{2 \pi}{3} , k \in \mathbb{Z}$

#### Explanation:

Here,

$2 \cos \theta + 1 = 0$

$\implies 2 \cos \theta = - 1$

$\cos \theta = - \frac{1}{2} < 0 \implies \cos \theta = \left(\pi - \frac{\pi}{3}\right) = \cos \left(\frac{2 \pi}{3}\right)$

So,

$\cos \theta = \cos \left(\frac{2 \pi}{3}\right) \to w h e r e , \theta = a r c \cos \left(- \frac{1}{2}\right) = \frac{2 \pi}{3}$

$\implies \theta = 2 k \pi \pm \frac{2 \pi}{3} , k \in \mathbb{Z}$