# How do you find the exact value of sin (x) when cos (x) = 3/5 and the terminal side of x is in quadrant 4?

Jun 5, 2018

See below

#### Explanation:

Remember that ${\sin}^{2} x + {\cos}^{2} x = 1$ for all x-value

If $\cos x = \frac{3}{5}$, then ${\cos}^{x} = 1 - {\sin}^{2} x = 1 - \frac{9}{25} = \frac{16}{25}$

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

However $x$ is in 4th quadrant where $\cos x$ is positive, we conclude that $\cos x = \frac{4}{5}$