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Math Help - Parametric Equations

  1. #1
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    Parametric Equations

    Thanks to those who realised that I had typed the question wrong... here is the correct version
    Please may someone help me solve this question:

    A curve is defined by the parametric equations
    x = 5 + 2cosθ, y = 3cos2θ

    a) Show that dy/dx = 6cosθ
    b) Verify that 2(y+3) = 3(x-5)^2 is a cartesian equation for the curve

    Thank you so much !
    Last edited by racheltllong; June 6th 2008 at 04:46 AM. Reason: incorrect question
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by racheltllong View Post
    Please may someone help me solve this question:

    A curve is defined by the parametric equations
    x = 5 + cos2θ, y = 3cos2θ

    a) Show that dy/dx = 6cosθ
    b) Verify that 2(y+3) = 3(x-5)^2 is a cartesian equation for the curve

    Thank you so much !
    Please check your question; what you are asked to show appears not to correspond to the parametric equation given.

    This is assuming that the equation is supposed to be:

    x = 5 + \cos^2(\theta),\ y = 3\cos^2(\theta),

    or even:

    x = 5 + \cos(2\theta),\ y = 3\cos(2\theta).

    RonL
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  3. #3
    Super Member ebaines's Avatar
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    You seem to have an error in your problem as written. Note that from what you provided:

    <br />
x = 5 + \cos (2 \theta)<br />

    <br />
\cos (2 \theta) = x - 5<br />

    <br />
y = 3 cos (2 \theta) = 3 (x-5) = 3x -15.<br />

    Hence dy/dx = 3, not 6 cos(\theta)<br />

    Please make corrections and repost.
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