Example 3: Intersection Area of Two Circles

Find the area of the region inside both the circles r = sin θ and r = cos θ.

The first thing to do is draw the graphs of both curves. The graphs are shown in Figure 7.9.8.

Figure 7.9.8

We see that the two circles intersect at the origin and at θ = π/4. The region is divided into two parts, one bounded by r = sin θ for 0 ≤ θ ≤ π/4 and the other bounded by r = cos θ for π/4 ≤ θ ≤ π/2. Thus