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Math Help - Convert from polar to rectangular

  1. #1
    Junior Member Greymalkin's Avatar
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    Convert from polar to rectangular

    r= sec^2{\theta\over 2}

    Book answer is: y^2=-4x+4
    How is it that you arrived at the answer? I've tried many ways and am no closer to the answer than when I started, please help.
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  2. #2
    MHF Contributor
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    Re: Convert from polar to rectangular

    Maybe there is an easier way, but... First express \sec^2(\theta/2) through \cos\theta using the double-angle formula. Then replace r by \sqrt{x^2+y^2} and \cos\theta by x/\sqrt{x^2+y^2} and simplify. It may be necessary to separately check special cases, such as when r = 0.
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    Re: Convert from polar to rectangular

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