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Thread: Polar coordinates to Cartesian coordinates

  1. #1
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    Polar coordinates to Cartesian coordinates

    Convert the system in the polar coordinates r'=(1-r), theta' =sin(theta/2)^2 into cartesian coordinates.
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  2. #2
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    Re: Polar coordinates to Cartesian coordinates

    Hey nm321.

    Can you show us your attempts?
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  3. #3
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    Re: Polar coordinates to Cartesian coordinates

    Polar coordinates to Cartesian coordinates-img_0675.jpg
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  4. #4
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    Re: Polar coordinates to Cartesian coordinates

    This is all I have so far. I'm stuck
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  5. #5
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    Re: Polar coordinates to Cartesian coordinates

    You have a linear transformation from one polar coordinate system to another: r'= 1- r and \theta'= sin^2(\theta/2). I would start by using the "half angle formula":
    sin(\theta/2)= \sqrt{(1/2)(1- cos(\theta)} so that \theta'= sin^2(\theta/2)= \frac{1}{2}(1- cos(\theta). Now use the fact that \theta= arctan\left(\frac{y}{x}\right), r= \sqrt{x^2+ y^2}, \theta'= arctan\left(\frac{y'}{x'}\right), and r'= \sqrt{x'^2+ y'^2}
    Last edited by HallsofIvy; Mar 12th 2016 at 07:18 AM.
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