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Math Help - Finding Tangent Line and Normal of a parametric equation

  1. #1
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    Finding Tangent Line and Normal of a parametric equation

    For \delta \mathbb{R}\rightarrow \mathbb{R}^2,\ t\ =\ \delta (t)\ =\ (cosh(2t-2),sin(2\pi t^2)) find the tangent line and the normal line passing through \delta(t_0),t_0\ =\ 1

    So i think the tangent line is T\delta (t_0)\ =\ \delta' (t_0)s\ +\ \delta (t_0)

    However Im clueless as to how to find the normal line.
    Last edited by CaptainBlack; January 14th 2012 at 02:31 AM. Reason: fix LaTeX
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  2. #2
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    Re: Finding Tangent Line and Normal of a parametric equation

    it's ok apparently, after pluggin in the to into the tangent equation to get Tdelta(to) = (x,y)s + (a,b) the normal line is simply Ndelta(to) = (-y,x)s + (a,b).
    ps it was meant to say deltaR rightarrow R to the power of 2 not that weird symbol.
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  3. #3
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    Re: Finding Tangent Line and Normal of a parametric equation

    \delta'(t_0) will be a two dimensional vector- the normal will be perpendicular to that so you just need a vector perpendicular to \delta'(t_0). In two dimensions, that's easy. A normal to the vector <a, b> is <b, -a>.
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