Spherical coordinates, angle question

1. Apr 9, 2009

gr3g1

Hey guys,
Im trying to figure out how the angles for the following sphere are obtained.

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

I understand that the integral is:

$\int_{0}^{\pi/2}\int_{\pi/4}^{?}\int_{0}^{2}$

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.

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. Apr 9, 2009

Billy Bob

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?