Math Project helpppp! Polar functions

[wowitsangie03]

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

I don't understand please helppp!

 

[MarkFL]

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

\(\displaystyle 2\cos(\theta)-1=0\) where \(\displaystyle -\frac{\pi}{2}<\theta<\frac{\pi}{2}\)