# How do you find the five remaining trigonometric function satisfying tantheta=-12/5, sintheta>0?

$\cos t = \pm \frac{5}{13}$
$\sin t = \left(\tan t\right) \left(\cos t\right) = \left(- \frac{12}{5}\right) \left(- \frac{5}{13}\right) = \frac{12}{13}$
$\cot t = \frac{1}{\tan} = - \frac{5}{12}$
$\sec t = \frac{1}{\cos} = - \frac{13}{5}$
$\csc t = \frac{1}{\sin} = \frac{13}{12}$