Question

Find the area of the region that lies inside both curves.

r = sin 2θ,     r = cos 2θ

Answer 1

Step 1 :

The curves are and .

First find out the intersection points of two curves.

General solution of is , where n is an integer.

If n = 0, then .

Step 2 :

Graph two curves in polar - coordinate plane.

Graph :

We can observe from the graph that the two curves intersect at 8 points.

There are 8 intersects on the interval .

Step 3 :

By symmetry area of the region that lies inside the both curves :

Area of the region that lies inside the both curves is square units.

Solution :

Area of the region that lies inside the both curves is square units.