What is the polar form of ( 5,9 )?

Jan 13, 2016

$\left(\sqrt{106} , 1.06\right)$

Explanation:

To convert from cartesian (x , y ) to polar ( r , theta )

use the following relationships :

${r}^{2} = {x}^{2} + {y}^{2} \Rightarrow r = \sqrt{{x}^{2} + {y}^{2}} , \theta = {\tan}^{-} 1 \left(\frac{y}{x}\right)$

using (5 , 9 ):

$r = \sqrt{{5}^{2} + {9}^{2}} = \sqrt{25 + 81} = \sqrt{106}$

and $\theta = {\tan}^{-} 1 \left(\frac{9}{5}\right) = 1.06$

rArr (5 , 9 ) → ( sqrt106 , 1.06 )