# What is the polar form of ( -7,1 )?

Jan 22, 2016

$\left(5 \sqrt{2} , 3\right)$

#### Explanation:

Use the following formulae linking Cartesian to Polar coordinates.

 • r^2 = x^2 + y^2

 • theta = tan^-1 (y/x )

[( - 7 , 1 ) is a point in the 2nd quadrant and care must be taken

to ensure that $\theta$ , is in the 2nd quadrant.]

so ${r}^{2} = {\left(- 7\right)}^{2} + {1}^{2} = 49 + 1 = 50 \Rightarrow r = \sqrt{50} = 5 \sqrt{2}$

and $\theta = {\tan}^{-} 1 = \left(\frac{1}{-} 7\right) = - 0.14 \textcolor{b l a c k}{\text{radians}}$

$\Rightarrow \theta = \left(\pi - 0.14\right) = 3 \textcolor{b l a c k}{\text{radians}}$