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Math Help - Parametrised by arc length

  1. #1
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    Parametrised curves

    Suppose that \alpha(t) is the parametrised curve given by

    \alpha(t) = \left(\begin{array}{c}sin^2(t)\\sin(t)cos(t)\end{a  rray}\right)

    for 0 \leq t \leq \pi.

    1. Show that \alpha(t) is parametrised by arc length.
    2. Find the length of \alpha(t).
    3. Find the normal vector to \alpha(t0) at where 0 < t0 < \pi.
    4. Do you recognise this curve?


    I don't have a clue what any of this means, the lecturer rushed through it and I won't have a chance to see her until Tuesday and this is in for Monday. Any help is much appreciated. Thanks.
    Last edited by Thomas154321; October 21st 2007 at 07:58 AM.
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  2. #2
    Super Member Rebesques's Avatar
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    For the first two, show that |\alpha'|=1 and calculate \int |\alpha'|. The third one is but an easy problem involving analytic geometry only. For the fourth one, call the coordinates x and y,
    and calculate an algebraic expression involving them.
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