# How do you use the point (-12,3) on the terminal side of the angle to evaluate the six trigonometric functions?

$\tan t = \frac{y}{x} = \frac{3}{-} 12 = - \frac{1}{4}$
${\cos}^{2} t = \frac{1}{1 + {\tan}^{2} t} = \frac{1}{1 + \frac{1}{16}} = \frac{16}{17}$
$\cos t = - \frac{4}{\sqrt{17}}$
$\sin t = \tan t . \cos t = \left(- \frac{1}{4}\right) \left(- \frac{4}{\sqrt{17}}\right) = \frac{1}{\sqrt{17}}$
$\cot t = \frac{1}{\tan t} = - 4$
$\sec t = \frac{1}{\cos t} = - \frac{\sqrt{17}}{4}$
$\csc t = \frac{1}{\sin t} = \sqrt{17}$