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Math Help - Parametric Equation (hard)

  1. #1
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    Parametric Equation (hard)

    am going to use % as alpha sign

    the parametric equations of the curve C are:

    x = a tan %
    y = a sec %

    dy/dx = sin%

    show that the equation of the tangent to C at pont P(a tan %, a sec %), where 0<%<(pie/2) is

    y = x sin% + a cos%
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  2. #2
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    Quote Originally Posted by Stylis10 View Post
    am going to use % as alpha sign

    the parametric equations of the curve C are:

    x = a tan %
    y = a sec %

    dy/dx = sin%

    show that the equation of the tangent to C at pont P(a tan %, a sec %), where 0<%<(pie/2) is

    y = x sin% + a cos%
    Use y - y1 = m(x - x1) as your model for the tangent line.

    Sub the known stuff in.

    Done that? Then you have to simplify a sec % - a sin % tan % and get a cos % .....

    a \sec \alpha - a \sin \alpha  \tan \alpha  = \frac{a - a \sin^2 \alpha }{\cos \alpha } = \frac{a(1 - \sin^2 \alpha )}{\cos \alpha } = ....
    Last edited by mr fantastic; February 24th 2008 at 04:09 AM. Reason: Replaced theta with alpha
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  3. #3
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    im still not getting it
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  4. #4
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    Quote Originally Posted by mr fantastic View Post
    Use y - y1 = m(x - x1) as your model for the tangent line.

    Sub the known stuff in.

    Done that? Then you have to simplify a sec % - a sin % tan % and get a cos % .....

    a \sec \alpha - a \sin \alpha  \tan \alpha  = \frac{a - a \sin^2 \alpha }{\cos \alpha } = \frac{a(1 - \sin^2 \alpha )}{\cos \alpha } = ....
    y - y1 = m(x - x1) is the standard slope-point form of a line.

    m is the gradient of the line. (x1, y1) is a known point on the line.

    You're given a point on the tangent, so x1 and y1 are known. And you've got dy/dx = m. So sub the stuff you know into the above:

    y - a \sec \alpha = \sin \alpha  (x - a \tan \alpha )

    \Rightarrow y - a \sec \alpha  = \sin \alpha  x - a \tan \alpha  \sin \alpha

    \Rightarrow y = \sin \alpha  x - a \tan \alpha  \sin \alpha  + a \sec \alpha .

    And I've already all but shown you that - a \tan \alpha  \sin \alpha  + a \sec \alpha simplifies to a \cos \alpha.
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  5. #5
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    oh thnxs, i get it now, i was trying to simplify sin% to get a numerical value for m.
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