# How do you find all six trigonometric function of theta if the point (-5,12) is on the terminal side of theta?

Feb 20, 2017

$\tan t = \frac{12}{-} 5$
${\cos}^{2} t = \frac{1}{1 + {\tan}^{2} t} = \frac{1}{1 + \frac{144}{25}} = \frac{25}{169}$
$\cos t = \pm \frac{5}{13}$
Because tan t < 0, then, cos t is negative
$\cos t = - \frac{5}{13}$
$\sin t = \tan t . \cos t = \left(- \frac{12}{5}\right) \left(- \frac{5}{13}\right) = \frac{12}{13}$
$\sec t = \frac{1}{\cos} = - \frac{13}{5}$
$\csc t = \frac{1}{\sin} = \frac{13}{12}$