# If tan theta=2/3 and cos theta >, how do you find sin theta?

May 25, 2018

$\sin t = \frac{2 \sqrt{13}}{13}$

#### Explanation:

$\tan t = \frac{2}{3}$ -->
$\cot t = \frac{1}{\tan t} = \frac{3}{2}$
${\sin}^{2} t = \frac{1}{1 + {\cot}^{2} t} = \frac{1}{1 + \frac{9}{4}} = \frac{4}{13}$
$\sin t = \pm \frac{2}{\sqrt{13}}$
Because tan t > 0 and cos t > 0, therefor, t lies in Quadrant 1 -->
and sin t is positive
$\sin t = \frac{2 \sqrt{13}}{13}$