# What is the polar form of ( -4,27 )?

Nov 9, 2016

$\left(27.29 , 1.72\right)$

#### Explanation:

The polar form is $\left(r , \theta\right)$
To find r use the formula ${r}^{2} = {x}^{2} + {y}^{2}$

$r = \sqrt{{\left(- 4\right)}^{2} + {27}^{2}} \approx 27.29$

To find $\theta$ use the formula $\tan \theta = \frac{y}{x}$ but make sure you look at the quadrant that the point is in to determine the right $\theta$ using the rules for the quadrants

$\tan \theta = \frac{27}{-} 4$

$\theta = {\tan}^{-} 1 \left(\frac{27}{-} 4\right) \approx - 1.423717971$ but the point is in quadrant two so we add $\pi$. Note that $\theta$ is usually in radian.

Hence, $\theta \approx 1.72$