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Spherical coordinates, angle question

  1. Apr 9, 2009 #1
    Hey guys,
    Im trying to figure out how the angles for the following sphere are obtained.


    [itex] x^{2} + y^{2} + z^{2} = 4, y = x, y = \sqrt[]{3}x, z = 0 [/itex]


    I understand that the integral is:

    [itex]\int_{0}^{\pi/2}\int_{\pi/4}^{?}\int_{0}^{2}[/itex]

    However, I cant not see how the "?" interval is found! I know it is using y = sqrt(3)*x
    pi/4 was determined because 90/2 = 45 degrees.

    Thanks in advance
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 9, 2009 #2
    Look at the xy plane from "above," and draw the region bounded by y=x, y=sqrt(3)*x, and the circle of radius 2 centered at origin. Where are the intersection points? Any famous angles?
     
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