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Math Help - Parametric Equation

  1. #1
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    Parametric Equation

    Eliminate t in the following equations to determine the type of curve represented.

    x = cos t , y= 1 - cos 2t

    I have so far managed to reduce the y=1-cos2t equation to 0 ? ,by using the addition formula and subing in x,to get rid of t.........but the ans is y= 2(1-x^2) ,-1<x<1.
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  2. #2
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    Remember that \cos{2t} = 2\cos^2{t} - 1.

    So y = 1 - \cos{2t}

     = 1 - (2\cos^2{t} - 1)

     = 1 - 2\cos^2{t} + 1

     = 2 - 2\cos^2{t}

     = 2 - 2x^2.


    I think you can see that this is a Quadratic, and since x = \cos{t} and -1 \leq \cos{t} \leq 1 for all t, that means -1 \leq x \leq 1.
    Last edited by Prove It; August 5th 2010 at 05:11 AM.
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    Thanks for that Prove It
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