# How do you find the value of costheta given sintheta=-3/5 and in quadrant IV?

Apr 23, 2018

$\cos \theta = \frac{4}{5}$

#### Explanation:

In quadrant IV, $\sin \theta$ is negative and $\cos \theta$ is positive. Keeping this in mind,

Recall the identity

${\sin}^{2} \theta + {\cos}^{2} \theta = 1$

We know $\sin \theta = \left(- \frac{3}{5}\right) , {\sin}^{2} \theta = {\left(- \frac{3}{5}\right)}^{2} = \frac{9}{25}$

Then,

$\frac{9}{25} + {\cos}^{2} \theta = \frac{25}{25}$

${\cos}^{2} \theta = \frac{25}{25} - \frac{9}{25}$

${\cos}^{2} \theta = \frac{16}{25}$

$\cos \theta = \pm \sqrt{\frac{16}{25}} = \pm \frac{4}{5}$

As we noted earlier, cosine is positive in quadrant IV, so we want the positive answer:

$\cos \theta = \frac{4}{5}$