# What is the polar form of (-3,3)?

Oct 16, 2016

From Cartesian form to polar form:

$\left(- 3 , 3\right) \to \left(3 \sqrt{2} , \frac{3 \pi}{4}\right)$

#### Explanation:

Because the x coordinate is negative, one must add $\pi$ to the inverse tangent function to obtain the correct angular component:

$\theta = {\tan}^{-} 1 \left(\frac{3}{-} 3\right) + \pi$

$\theta = \frac{3 \pi}{4}$

$r = \sqrt{{\left(- 3\right)}^{2} + {3}^{2}}$

$r = \sqrt{18} = 3 \sqrt{2}$