# If cos theta=-3/4 and tan theta is negative, how do you find the value of sin theta?

Mar 27, 2018

$\sin \theta = \frac{\sqrt{7}}{4}$

#### Explanation:

$\text{given "costheta<0rArr"second/third quadrant}$

$\text{given "tantheta<0rArr" second/fourth quadrant}$

$\Rightarrow \theta \text{ is in second quadrant where } \sin \theta > 0$

•color(white)(x)sin^2theta+cos^2theta=1

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

$\text{since "sintheta>0" then}$

$\sin \theta = \sqrt{1 - {\left(- \frac{3}{4}\right)}^{2}}$

$\textcolor{w h i t e}{\sin \theta} = \sqrt{1 - \frac{9}{16}} = \sqrt{\frac{7}{16}}$

$\Rightarrow \sin \theta = \frac{\sqrt{7}}{4}$