# Conversion of polar to cartesian

#### Bowlbase

I'm getting pretty frustrate with polar coordinates and I can't find any videos online that are very helpful. So I have this and a few other questions I'm posting.

The first problem, I thought, would be simple but my graphs dont match:
Convert$$\displaystyle r=sin(2 \theta)$$ into cartesian
1. I changed it to $$\displaystyle r=2sin(\theta) cos(\theta)$$
2. Then multiplied by r twice $$\displaystyle r^3=2rsin(\theta) rcos(\theta)$$
3. $$\displaystyle x=rcos(\theta)$$ and $$\displaystyle y=rsin(\theta)$$
4. so: $$\displaystyle r^3=2xy$$
5. and since $$\displaystyle r^2=x^2+y^2$$
6. finally I get: $$\displaystyle (x^2+y^2)(\sqrt(x^2+y^2))=2xy$$

The graphs do not match so I'm getting desperate to find my mistake here.

#### skeeter

MHF Helper
$$\displaystyle r = \pm \sqrt{x^2+y^2}$$

you have to graph ...

$$\displaystyle (x^2+y^2)^{3/2} = 2xy$$ (note that this equation graphs in quads I and III)

and

$$\displaystyle -(x^2+y^2)^{3/2} = 2xy$$ (graphs in quads II and IV)

• 1 person

#### Bowlbase

Okay, I have the method correct then, I just have to remember to do both signs.

Thanks for the help.