# How do you find y if the point (5,y) is on the terminal side of theta and costheta=5/13?

Dec 2, 2017

$y = \pm 12$

#### Explanation:

$\cos t = \frac{5}{13}$
$\sin t = \frac{y}{13}$
Use trig identity:
${\sin}^{2} t + {\cos}^{2} t = 1$
${y}^{2} / 169 + \frac{25}{169} = 1$
${y}^{2} + 25 = 169$
${y}^{2} = 169 - 25 = 144$
$y = \pm 12$
There are 2 arcs (or angles) t that have the same cos value (5/13).