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Math Help - a cone equation

  1. #1
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    a cone equation

    Show that r(t)=tsin(pi*t)i + tj +tcos(pi*t)k lies on a cone, find the equation for this cone and sketch it.

    How should I solve this question? Thank you very much.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Jenny20 View Post
    Show that r(t)=tsin(pi*t)i + tj +tcos(pi*t)k lies on a cone, find the equation for this cone and sketch it.

    How should I solve this question? Thank you very much.
    Convert it to coordinate form:

    x = t sin(pi*t)

    y = t

    z = t cos(pi*t)

    Now eliminate t:

    x^2+z^2= t^2 [sin^2(pi*t) + cos^2(pi*t)] = t^2 = y^2

    or:

    x^2 + z^2 = y^2

    which is a cone with its axis horizontal.

    RonL
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  3. #3
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    thank you !
    Last edited by Jenny20; February 22nd 2007 at 12:13 PM.
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