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

Mar 18, 2017

$\tan t = \frac{n}{m}$
${\cos}^{2} t = \frac{1}{1 + {\tan}^{2} t} = \frac{1}{1 + {n}^{2} / \left({m}^{2}\right)} = {m}^{2} / \left({m}^{2} + {n}^{2}\right)$
$\cos t = \pm \frac{m}{\sqrt{{m}^{2} + {n}^{2}}}$
${\sin}^{2} t = \frac{1}{1 + {\cot}^{2} t} = \frac{1}{1 + \frac{m}{n}} = {n}^{2} / \left({m}^{2} + {n}^{2}\right)$
sin t = +- n/(sqrt(m^2 + n^2)
$\tan t = \frac{n}{m}$
$\cot t = \frac{m}{n}$
$\sec t = \pm \frac{\sqrt{{m}^{2} + {n}^{2}}}{m}$
$\csc t = \pm \frac{\sqrt{{m}^{2} + {n}^{2}}}{n}$