# What is the polar form of (-5,13)?

Jan 17, 2016

$\left(\sqrt{194} , 1.94\right)$

#### Explanation:

Using the formulae that links Cartesian and Polar coordinates.

• x^2 + y^2 = r^2

• x = rcostheta

• y = rsintheta

• theta = tan^-1 (y/x )

${r}^{2} = {\left(- 5\right)}^{2} + {13}^{2} = 194 \Rightarrow r = \sqrt{194}$

$\theta = {\tan}^{-} 1 \left(\frac{13}{-} 5\right) = - 1.2$

(- 5 , 13 ) is in 2nd quadrant and so $\theta = \pi - 1.2 = 1.94$