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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Originally Posted by Jenny20 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
thank you !
Last edited by Jenny20; February 22nd 2007 at 12:13 PM.
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