Given point (12,-9) how do you find the distance of the point from the origin, then find the measure of the angle in standard position whose terminal side contains the point?

Dec 27, 2016

$r = 15 , \angle x O P = 2 \pi - \arctan \frac{3}{4}$

Explanation:

The old and good formulas.

$x = r \cos t = 12$
$y = r \sin t = - 9$

${x}^{2} + {y}^{2} = {r}^{2} = 144 + 81 = 225$
$r = 15$

$\frac{y}{x} = \tan t = - \frac{9}{12} = - \frac{3}{4}$

$t = - \arctan 0.75$

$\tan \left(- \theta\right) = - \tan \theta = \tan \left(2 \pi - \theta\right)$