Conversion of polar to cartesian

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 into cartesian

1. I changed it to

2. Then multiplied by r twice

3. and

4. so:

5. and since

6. finally I get:

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

Re: Conversion of polar to cartesian

you have to graph ...

(note that this equation graphs in quads I and III)

and

(graphs in quads II and IV)

Re: Conversion of polar to cartesian

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

Thanks for the help.