# What is the polar form of ( -4,6 )?

Oct 18, 2017

$\left(- 4 , 6\right) = \left(2 \sqrt{13} , - 0.923\right)$

#### Explanation:

For any point $P \left(a , b\right)$ in the Cartesian plane, we can convert it to polar form $\left(r , \vartheta\right)$ using the following formulae

$r = \sqrt{{a}^{2} + {b}^{2}}$

$\vartheta = \arctan \left(\frac{b}{a}\right)$

$\therefore r = \sqrt{- {4}^{2} + {6}^{2}} = 2 \sqrt{13}$ and $\vartheta = \arctan \left(- \frac{4}{6}\right) = - 0.923$

$\therefore \left(- 4 , 6\right) = \left(2 \sqrt{13} , - 0.923\right)$