# If tan theta = 24/7, 180 < theta < 270 how do you find cos theta?

Jun 29, 2016

$- \frac{7}{25}$

#### Explanation:

$\theta$ is in the third quadrant wherein tan is positive and both sin

and cos are negative.

$\tan \theta = \frac{24}{7} = \sin \frac{\theta}{\cos} \theta = \frac{\sqrt{1 - {\cos}^{2} \theta}}{\cos} \theta$

Squaring and solving, $\cos \theta = \pm \frac{7}{25.}$.