Thread: Inner Loop of a limacon

The polar function, r(theta)=2 cos(theta)-1, is a limacon. It has an outer and inner loop. Find the exact values , a and b, such that a <=theta<=b creates the inner loop of the limacon.

I know that r= a+- bcos(theta) so i guess that means its -1/2 and that means 2pi/3 and 4pi/3

I need help.

If you look at a plot of the curve, you see you want to solve for:

where