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Math Help - urgent help please - sphere

  1. #1
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    Question urgent help please - sphere

    Show why (x,y,z) = (a*sin(phi)* cos(theta) , a*sin(phi)* sin(theta), sqrt(3)*a*sin(phi) ) lies on the sphere of radius 2a centered at origin.
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  2. #2
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    Quote Originally Posted by Jenny20 View Post
    Show why (x,y,z) = (a*sin(phi)* cos(theta) , a*sin(phi)* sin(theta), sqrt(3)*a*sin(phi) ) lies on the sphere of radius 2a centered at origin.
    I'm not getting a result that says it's on this sphere:

    Find the distance between this point and the origin:

    d = \sqrt{(asin(\phi)cos(\theta) - 0)^2 + (asin(\phi)sin(\theta) - 0)^2 + (\sqrt{3}asin(\phi) - 0)^2}

    d = \sqrt{a^2sin^2(\phi)cos^2(\theta) + a^2sin^2(\phi)sin^2(\theta) + 3a^2sin^2(\phi)}

    d = \sqrt{a^2sin^2(\phi)[cos^2(\theta) + sin^2(\theta)] + 3a^2sin^2(\phi)}

    d = \sqrt{a^2sin^2(\phi) + 3a^2sin^2(\phi)}

    d = \sqrt{4a^2sin^2(\phi)}

    d = |2asin(\phi)|

    For this point to be on the sphere centered at the origin with a radius of 2a this distance would have to be 2a.

    -Dan
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  3. #3
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    Quote Originally Posted by topsquark View Post
    d = |2asin(\phi)|

    For this point to be on the sphere centered at the origin with a radius of 2a this distance would have to be 2a.
    I think this shows that,
    -1\leq d\leq 1.
    Those all the points in in the sphere though not necessarility on it.
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  4. #4
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    Thank you very much !
    Last edited by Jenny20; January 16th 2007 at 09:12 AM.
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