Polar integration

[tandoorichicken]

Find the area of the region common to r=4\sin\theta and r=4\cos\theta

How can I find the limits of integration? I know one of the limits is pi/4 by setting r1 = r2 but I can't find the other one because it is different for each equation. The graph shows it intersecting at (0,0), but thats a different theta for each equation.

[HallsofIvy]

The easy way to do this is to use the symmetry. Integrate r= 4 sin(\theta) for \theta= 0 to \frac{\pi}{4}, then double it.