Convert to Cartesian Coordinates? r= sin(2theta)

Question

anonymous · Answer

do you know the answer? mine is coming out goofy

hitaro9 · Answer

I know that a squareroot is involved. Webassign says "Right the answer so any square root has a positive coefficient"

hitaro9 · Answer

Write*

anonymous · Answer

i put $\sin(2\theta)=2\cos(\theta)\sin(\theta)$ and got 
$$r=2\sin(\theta)\cos(\theta)$$ then replaced $\cos(\theta)$ by $\frac{x}{r}$ and $\sin(\theta)$ by $\frac{y}{r}$ and got 
$$r=2\frac{xy}{r^2}$$ then 
$$r^3=2xy$$ or 
$$(x^2+y^2)\sqrt{x^2+y^2}=2xy$$ but that looks goofy to me

hitaro9 · Answer

I'm seeing the logic, but yeah. Most of the other answers have worked out very well and looked a lot simpler.

anonymous · Answer

compare http://www.wolframalpha.com/input/?i=%28x^2%2By^2%29 \sqrt{x^2%2By^2}%3D2xy http://www.wolframalpha.com/input/?i=r+%3D+sin%282+theta%29

anonymous · Answer

think i missed at $\pm$

hitaro9 · Answer

I'm gunna go ahead and enter what you put in to webassign. If it works out, then I guess it was just a complicated answer.

anonymous · Answer

gotta love webassign
good luck!

hitaro9 · Answer

Yep. It worked out. Thanks a ton dude.