The limacon has an inner loop when .


(a) When , determine the range of values of that correspond to the inner loop. For your answer, list the values of where at which the loop begins and ends, giving these values in increasing order. Your answer may depend on .

Smaller value of :

Larger value of :


(b) When , determine the range of values of that correspond to the inner loop. For your answer, list the values of where at which the loop begins and ends, giving these values in increasing order. Your answer may depend on .

Smaller value of :

Larger value of :

You can earn partial credit on this problem.