# What is the polar form of ( -27,15 )?

Jan 23, 2016

$\left(\sqrt{954} , 2.63\right)$

#### Explanation:

Use the following formulae that links Cartesian to Polar coordinates.

 • r^2 = x^2 + y^2

• theta = tan^-1 (y/x)

Here x = - 27 and y = 15 .[ Note also that (-27 , 15 ) is a point in

the 2nd quadrant and so care must be taken to ensure $\theta$

${r}^{2} = {\left(- 27\right)}^{2} + {\left(15\right)}^{2} = 729 + 225 = 954$

$\Rightarrow r = \sqrt{954}$

$\theta = {\tan}^{-} 1 \left(\frac{15}{-} 27\right) = - 0.51 \textcolor{b l a c k}{\text{radians}}$

To find $\theta \textcolor{b l a c k}{\text{ in the 2nd quadrant}}$

$\theta = \left(\pi - 0.51\right) = 2.63 \textcolor{b l a c k}{\text{ radians}}$

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