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Thread: Convert to polar coordinates

  1. #1
    Apr 2018

    Convert to polar coordinates

    How would I convert to polar coordinates?

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  2. #2
    MHF Contributor

    Apr 2005

    Re: Convert to polar coordinates

    For a point represented as (x, y) in Cartesian coordinates and as $\displaystyle (r, \theta)$ in polar coordinates,
    $\displaystyle x= r cos(\theta)$
    $\displaystyle y= r sin(\theta)$
    (I would think that would be one of the first things you would learn about polar coordinates.)

    So $\displaystyle x^2+ y^2= (x^2+ y^2- x)^2$ immediately becomes $\displaystyle r^2 cos^2(\theta)+ r^2 sin^2(\theta)= (r^2 cos^2(\theta)+ r^2 sin^2(\theta)- r sin(\theta))^2$.

    Of course $\displaystyle x^2+ y^2= r^2 cos^2(\theta)+ r^2 sin^2(\theta)= r^2(cos^2(\theta)+ sin^2(\theta))= r^2$ so this is $\displaystyle r^2= (r^2- r sin(\theta))^2$.

    We can factor $\displaystyle r^2$ out of the right side and, as long as r is not 0, cancel on both sides. That leaves $\displaystyle (r- sin(\theta))^2= 1$.
    Thanks from topsquark
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