# How do you find the exact values of other 5 trigonometric functions given sin u = -5/13 and cos u>0?

May 28, 2016

Find values of trig functions

#### Explanation:

Apply the trig identity: ${\cos}^{2} x = 1 - {\sin}^{2} x$
${\cos}^{2} u = 1 - {\sin}^{2} u = 1 - \frac{25}{169} = \frac{144}{169}$
$\cos u = \frac{12}{13}$ (cos u positive)
$\tan u = \frac{\sin}{\cos} = - \frac{5}{12}$
$\cot u = \frac{1}{\tan} = - \frac{12}{5}$
$\sec u = \frac{1}{\cos} = \frac{13}{12}$
$\csc u = \frac{1}{\sin} = - \frac{13}{5}$