# What is the polar form of (-5,3)?

Feb 22, 2016

$\left(\sqrt{34} , 2.6\right)$

#### Explanation:

Using the formulae that links Cartesian to Polar coordinates.

• r^2 = x^2 + y^2

• theta = tan^-1(y/x)

here x = - 5 and y = 3

$\text{ hence } {r}^{2} = {\left(- 5\right)}^{2} + {3}^{2} = 25 + 9 = 34 \Rightarrow r = \sqrt{34}$

Now the point (-5,3) is in the 2nd quadrant so care must be taken to ensure $\theta \text{ is in the 2nd quadrant }$

$\theta = {\tan}^{-} 1 \left(- \frac{3}{5}\right) = - 0.54 \text{ radians }$

rArr theta = (pi - 0.54 ) ≈ 2.6" radians "