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Math Help - unit tangent vector

  1. #1
    Junior Member SirOJ's Avatar
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    unit tangent vector

    im trying to find the unit tangent vector of an elipse of the form
     x = acos(t)   y= asin(t) at  t = \pi

    Do i firstly need to get the coordinates in non-parametric form i.e.
    use the equation of an elipse?
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  2. #2
    Super Member
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    For ellipse x = a*cosφ, and y = a*sinφ is not possible. I think it should be
    y = b*sinφ.
    To find the tangent vector, write the equation of the ellipse in the standard form and proceed.
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  3. #3
    MHF Contributor

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    Well, if you consider a circle to be a special case of an ellipse?


    If you meant x= a cos(t), y= b sin(t) then you can do the following: [tex]\frac{dy}{dx}= \frac{\frac{dy}{dt}}{\frac{dx}{dt}= \frac{b cos(t)}{-a sin(t)}[tex]. At t= \pi, [tex] \frac{dy}{dt}= cos(t)= cos(\pi)= -1 and \frac{dx}{dt}= -a sin(t)= -a sin(\pi)= 0 so the slope does not exist. The tangent line at t= \pi is the vertical line x= -a. The unit tangent vector is -\vec{j}.
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