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Math Help - Conversion of polar to cartesian

  1. #1
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    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 r=sin(2 \theta) into cartesian
    1. I changed it to r=2sin(\theta) cos(\theta)
    2. Then multiplied by r twice r^3=2rsin(\theta) rcos(\theta)
    3. x=rcos(\theta) and y=rsin(\theta)
    4. so: r^3=2xy
    5. and since r^2=x^2+y^2
    6. finally I get: (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.
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  2. #2
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    Re: Conversion of polar to cartesian

    r = \pm \sqrt{x^2+y^2}

    you have to graph ...

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

    and

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