How do you sketch the angle whose terminal side in standard position passes through (5,12) and how do you find sin and cos?

Mar 12, 2017

$\sin t = \frac{12}{13}$
$\cos t = \frac{5}{13}$

Explanation:

The terminal side of this angle t is in Quadrant 1.
$\tan t = \frac{12}{5}$
Use trig identity:
${\cos}^{2} t = \frac{1}{1 + {\tan}^{2} t} = \frac{1}{1 + \frac{144}{25}} = \frac{25}{169}$
$\cos t = \pm \frac{5}{13}$
Because t is in Quadrant 1, take the positive value.
$\sin t = \tan t . \cos t = \left(\frac{12}{5}\right) \left(\frac{5}{13}\right) = \frac{12}{13}$