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Math Help - Relating X and Y

  1. #1
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    Relating X and Y

    Eliminate t to give an equation that relates x and y:
    x=cos(t)y=sin2(t)−3

    y= ??
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  2. #2
    Super Member Aryth's Avatar
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    Remember the identity:

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

    So:

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

    y = 1 - \cos^2{t} - 3

    y = -\cos^2{t} - 2

    Now we look at x:

    x = \cos{t}

    Square both sides:

    x^2 = \cos^2{t}

    Multiply both sides by -1:

    -x^2 = -\cos^2{t}

    Now, subtract both sides by 2:

    -x^2 - 2 = -\cos^2{t} - 2

    We know that:

    y = -\cos^2{t} - 2

    So, we get:

    y = -x^2 - 2

    And there you go.
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  3. #3
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    Quote Originally Posted by gearshifter View Post
    Eliminate t to give an equation that relates x and y:
    x=cos(t)y=sin2(t)−3

    y= ??
    Here is a slightly different attempt:

    x = \cos(t)~\implies~x^2=\cos^2(t)

    y = \sin^2(t)-3~\implies~y+3=\sin^2(t)

    Add columnwise:

    y+3+x^2=\sin^2(t)+\cos^2(t)=1~\implies~\boxed{y=-x^2-2}
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  4. #4
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    wow thanks. I was stuck on that for sometime because i didnt know how to relate it!
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