Question

Consider the region R inside the graph of r = 2cos θ and outside the graph of r = 2 − 2cos θ.

Find the values α and β of θ in [−π, π] corresponding to the points at which the graphs intersect, with α < β and then find the area A of the region R.

Answer 1

To find the points of intersection, set the functions equal to each other and solve for theta.

Answer 2

2-2costeta=2costeta
teta=+-pi/3

Answer 3

I have nothing that to sketch the area.