# What is cos(arc sin (5/13))?

May 5, 2018

12/13

#### Explanation:

Call x the arc (angle) whose sin is $\left(\frac{5}{13}\right)$
sin x = 5/13, find cos x.
$c {o}^{2} x = 1 - {\sin}^{2} x = 1 - \frac{25}{169} = \frac{144}{169}$
$\cos x = \pm \frac{12}{13}$
Since x is in Quadrant 1 ($\sin x = \frac{5}{13}$), then, cos x is positive.
$\cos x = \frac{12}{13}$