# What is the polar form of ( 36,48 )?

Sep 10, 2016

Polar form of $\left(36 , 48\right)$ is $\left(60 , {53.13}^{o}\right)$

#### Explanation:

Polar coordinates $\left(r , \theta\right)$ are related to Cartesian coordinates $\left(x , y\right)$ by the following:

$x = r \cos \theta$, $y = r \sin \theta$ and ${r}^{2} = {x}^{2} + {y}^{2}$

Hence, let polar coordinates of $\left(36 , 48\right)$ be $\left(r , \theta\right)$

Hence $r = \sqrt{{36}^{2} + {48}^{2}} = \sqrt{1296 + 2304} = \sqrt{3600} = 60$

$\cos \theta = \frac{36}{60} = 0.60$ and $\sin \theta = \frac{48}{60} = 0.80$

and from tables $\theta = {53.13}^{o}$

Hence, polar form of $\left(36 , 48\right)$ is $\left(60 , {53.13}^{o}\right)$