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Spherical cordinates?

  1. Nov 19, 2009 #1
    1. The problem statement, all variables and given/known data

    Find a parametric representation for the part of the sphere x^2 + y^2 + z^2 = 64 that lies between the planes z = -4 and z = 4.

    i have found
    x = 8sin(ϕ)cos(θ)
    y = 8sin(ϕ)sin(θ)
    z= 8cos(ϕ)

    0 ≤ θ ≤ 2π (n looking thing is pi)

    now i need to find the bounds of ϕ

    i know under perfect conditions they are 0 to π
    but these are not perfect conditions and im not sure how to find them exactly?
  2. jcsd
  3. Nov 19, 2009 #2
    nevermind i got it.
    what you do is take your z component and set it equal to you plane so
    8cos(ϕ) = 4 you get cos(ϕ)=.5 so you get ϕ= pi/3
    then by symmetry you know your lower bound will be pi - (pi/3) which give you 2pi/3
    these are the correct bounds :)
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