# How do you convert r \sin^2 \theta =3 \cos \theta into rectangular form?

Apr 11, 2018

The rectangular form is ${y}^{2} = 3 x$

#### Explanation:

To convert from polar coordinates to rectangular coordinates, apply the following

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

$\cos \theta = \frac{x}{r}$

$\tan \theta = \frac{y}{x}$

and

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

Therefore,

$r {\sin}^{2} \theta = 3 \cos \theta$

$\iff$, $r \cdot {y}^{2} / {r}^{2} = 3 \frac{x}{r}$

$\iff$, ${y}^{2} = 3 x$

This is the equation of a parabola.

graph{(y^2-3x)=0 [-3.375, 16.625, -4.36, 5.64]}