# Math Help - polar conversion

1. ## polar conversion

I can't figure how to convert this polar equation to a cartesian equation.
$r = 2 - \sin2\theta$

2. Originally Posted by cubs3205
I can't figure how to convert this polar equation to a cartesian equation.
$r = 2 - \sin2\theta$
$r = 2 - \sin 2 \theta$ .............................simplify the double angle sine

$\Rightarrow r = 2 - 2 \sin \theta \cos \theta$ .................multiply through by $r^2$

$\Rightarrow r^3 = 2r^2 - 2r \sin \theta \cdot r \cos \theta$ ........now convert

$\Rightarrow \left( x^2 + y^2 \right)^{3/2} = 2x^2 + 2y^2 - 2xy$

and you can attempt to simplify that monstrosity if you so desire, i would leave it like that though