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Homework Help: Parametric representation

  1. Dec 6, 2005 #1
    Find the parametric representation for the surface:
    The part of the sphere x^2 + y^2 + z^2 = 16 that lies between the planes z = -2 and z = 2.

    okay, i know that i have to use spherical coordinates which is
    x = 4sin(phi)cos(theta)
    y = 4sin(phi)sin(phi)
    z = 4cos(phi)

    i know how to find the interval for phi, but how do you find the interval for theta? this is probably a stupid question, but i don't get it.
  2. jcsd
  3. Dec 6, 2005 #2
    That should be y=4sin(phi)sin(theta).
    What is theta on the sphere ? If you set phi to some constant, what curve results on the sphere's surface ? What does this imply about the restriction on theta ?
  4. Dec 7, 2005 #3


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    Remember that [itex]\theta[/itex] measures the angle in a plane parallel to the xy plane. Imagine the sphere cut by such a plane for z between -2 and 2. What restrictions are there on [itex]\theta[/itex]?
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