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Math Help - Parametric equations.

  1. #1
    Junior Member
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    Parametric equations.

    The following problem problem I need help with:-

    The parametric curve de ned by the equations
    x
    (t) = cos(t); y(t) = sin(3t); 0 <=t <= 2:

    a) Find a formula which represents the slope of the tangent line to the curve at the point (
    x(t); y(t)):

    b) Find the points (values of
    t and corresponding (x; y) coordinates) where the curve has a horizontal tangent line, and nd the points where the curve has a vertical tangent line.
    c) Use the information you found in part b) to draw a sketch of the curve.
    d) Set-up,
    but do not compute, an integral that represents the length of this parametric curve.

    Last edited by mr fantastic; April 24th 2010 at 02:22 PM. Reason: Re-titled.
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  2. #2
    MHF Contributor

    Joined
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    [QUOTE=Sally_Math;500410]
    The following problem problem I need help with:-

    The parametric curve de ned by the equations
    x
    (t) = cos(t); y(t) = sin(3t); 0 <=t <= 2:

    a) Find a formula which represents the slope of the tangent line to the curve at the point (
    x(t); y(t)):

    The "slope of the tangent line" is \frac{dy}{dx}= \frac{\frac{dy}{dt}}{\frac{dx}{dt}}

    b) Find the points (values of
    t and corresponding (x; y) coordinates) where the curve has a horizontal tangent line, and nd the points where the curve has a vertical tangent line.

    The tangent line will be horizontal when \frac{dy}{dt}= 0 and vertical when \frac{dx}{dt}= 0.

    c) Use the information you found in part b) to draw a sketch of the curve.
    d) Set-up,
    but do not compute, an integral that represents the length of this parametric curve.

    \int \sqrt{(\frac{dx}{dt})^2+ \frac{dy}{dt})^2} dt
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