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Math Help - parameterized curves that lie in R3

  1. #1
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    parameterized curves that lie in R3

    which image of the given parameterized curves lie on the unit sphere in R3?

    1. r(x)=(sin(3x), 0, cos(3x))
    2. r(x)=(x^2, cos x, sin x)
    3. r(x)=(1/sqrt.2, (-cos x)/sqrt.2, (sin x)/sqrt.2)
    4. r(x)= (sec x, 1/sqrt.2, cos x)

    How do you actually go about determining this?
    Last edited by Taurus3; February 13th 2011 at 11:53 PM.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    For a given parametrized curve r(t)=(x(t),y(t),z(t)) the image lie on the unit sphere of \mathbb{R}^3 iff x(t)^2+y(t)^2+z(t)^2=1 for all t . For example r(t)=(\sin 3t,0,\cos 3t) satisfies it because \sin^2 3t+0^2+\cos^2 3t=1 for all t.


    Fernando Revilla
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