# How do you convert (17,-2) into polar coordinates?

Jul 6, 2018

The polar coordinates are $= \left(17.12 , - {6.71}^{\circ}\right)$

#### Explanation:

To convert from rectangular coordinates $\left(x , y\right)$ to polar coordinates $\left(r , \theta\right)$, apply the following

$\left\{\begin{matrix}x = r \cos \theta \\ y = r \sin \theta \\ r = \sqrt{{x}^{2} + {y}^{2}} \\ \tan \theta = \frac{y}{x}\end{matrix}\right.$

Here,

The rectangular coordinates are $= \left(17 , - 2\right)$

$r = \sqrt{{\left(17\right)}^{2} + {\left(- 2\right)}^{2}} = \sqrt{293} = 17.12$

And

$\theta = \arctan \left(- \frac{2}{17}\right) = - {6.71}^{\circ}$

The polar coordinates are $= \left(17.12 , - {6.71}^{\circ}\right)$