# What is the polar form of (5,-3)?

Dec 6, 2015

$r = \sqrt{{x}^{2} + {y}^{2}}$

$\theta = {\tan}^{-} 1 \left(\frac{y}{x}\right)$

#### Explanation:

First note, the coordinate $\left(5. - 3\right)$ is in Quadrant IV so $270 < \theta < 360$

$r = \sqrt{{5}^{2} + {\left(- 3\right)}^{2}} = \sqrt{34}$

Reference Angle in Quad IV $= {\tan}^{-} 1 \left(\frac{3}{5}\right) \approx {31}^{o}$

$\theta = \left({270}^{o}\right) +$ (reference angle) $= 270 + 31 = {301}^{o}$

polar form $= \left(\sqrt{34} , {301}^{o}\right)$

hope that helped