# What is (5,8) in polar coordinates?

Nov 24, 2016

The polar coordinates would be $\left(r , \theta\right)$ or $\left(\sqrt{89} , \theta\right)$ where $\theta$ is defined by the relation $\tan \theta = 1.6$

#### Explanation:

Cartesean and Polar coordinates are related by x= $r \cos \theta$ and y=$r \sin \theta$

Hence $r \cos \theta = 5$
$r \sin \theta = 8$

Squaring and adding the above two equations would give ${r}^{2} = 89$ thus r= $\sqrt{89}$

Dividing the second equation by the first one would give $\tan \theta = \frac{8}{5} = 1.6$

The polar coordinates would be $\left(r , \theta\right)$ or $\left(\sqrt{89} , \theta\right)$ where $\theta$ is defined by the relation $\tan \theta = 1.6$