# How do you convert  r = csc^2 (theta)  into cartesian form?

Aug 21, 2016

${y}^{4} = {x}^{2} + {y}^{2}$

#### Explanation:

The relation between polar coordinates $\left(r , \theta\right)$ and Cartesian coordinates $\left(x , y\right)$ is given by $x = r \cos \theta$, $y = r \sin \theta$ and $r = \sqrt{{x}^{2} + {y}^{2}}$.

Hence, $r = {\csc}^{2} \theta$

$\Leftrightarrow \frac{y}{\sin} \theta = {\csc}^{2} \theta$

or y=sintheta×csc^2theta

or $y = \frac{1}{\sin} \theta = \frac{r}{y}$

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

or ${y}^{4} = {x}^{2} + {y}^{2}$