# How do you convert the Cartesian coordinates (20,3) to polar coordinates?

How do you convert the Cartesian coordinates (20,3) to polar coordinates?

ReportAnswer 1

$\sqrt{409} \angle 8 , {53}^{\circ}$

#### Explanation:

Any point $\left(x , y\right)$ in rectangular form may be converted into polar form $\left(r , \theta\right)$ as follows

$r = \sqrt{{x}^{2} + {y}^{2}}$

$\theta = {\tan}^{- 1} \left(\frac{y}{x}\right)$

Where $\theta$ is always measured anti-clockwise from the positive x-axis.

So in this case, $r = \sqrt{{20}^{2} + {3}^{2}} = \sqrt{409}$

$\theta = {\tan}^{- 1} \left(\frac{3}{20}\right) = 8 , {53}^{\circ}$

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