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Calculus III help!

  1. Nov 4, 2006 #1
    I really have difficulty with spherical coordinates graphings. can someone help me with this problem?

    Sketch the solid consisting of all points with spherical coordinates (ρ,θ,φ) such that 0≤ θ ≤π/2, 0≤ φ ≤π/6, and 0≤ ρ ≤2cosφ

    thanks so much!

    i think this looks like a bowl with radius ρ= root 3,
    then I don't understand how to graph theta and phi according to that range. that's where i got stuck.
    Last edited: Nov 4, 2006
  2. jcsd
  3. Nov 4, 2006 #2


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    The "range" of ρ is dependant upon the value of φ. So if you start at φ=0. At this point, all the ρ btw 0 and 2 are permitted. But as φ progresses towards π/6, ρ can ony take value btw 0 and 2cosφ. And at φ=π/6, it can only take values btw 0 and [itex]\sqrt{3}[/itex]. In btw, the range of rho decrease as cosφ decreases btw 0 and π/6, i.e. very slowly at the begining (the crest of the cos) and then steadily until π/6.

    Now that you've got the range of ρ and φ covered, just complete the volume by making θ vary.
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