# How do you convert r² = costheta into polar form?

##### 1 Answer
May 31, 2016

$\left(\sqrt{\cos \left(\theta\right)} , \theta\right)$

#### Explanation:

Standard polar form is of format $\left(r , \theta\right)$

Where $y = r \sin \left(\theta\right) \text{ and } x = r \cos \left(\theta\right)$
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Notice that in the question we have ${r}^{2} \to r = \sqrt{{r}^{2}} = \sqrt{\cos \left(\theta\right)}$

Implying that standard form of $y = r \sin \left(\theta\right)$ translates into $y = \sqrt{\cos \left(\theta\right)} \times \sin \left(\theta\right)$

Implying that the standard form of $x = r \cos \left(\theta\right)$ translates into $x = \sqrt{\cos \left(\theta\right)} \times \cos \left(\theta\right)$

So in polar form of type $\left(r , \theta\right)$ we have:

$\left(\sqrt{\cos \left(\theta\right)} , \theta\right)$