# If cos=(-5/13), tan theta > 0, what is sin theta?

Jun 27, 2016

$\sin \theta = - \frac{12}{13}$

#### Explanation:

If $\cos \theta < 0$ and $\tan \theta > 0$

then $\theta$ is in the third quadrant, where $\sin \theta < 0$

$\sin \theta = - \sqrt{1 - {\cos}^{2} \theta}$

$\sin \theta = - \sqrt{1 - {\left(\frac{5}{13}\right)}^{2}}$

$\sin \theta = - \sqrt{1 - \frac{25}{169}}$

$\sin \theta = - \sqrt{\frac{144}{169}}$

$\sin \theta = - \frac{12}{13}$