The limacon $r=1+c\sin(\theta)$ has an inner loop when $|c|>1$.

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(a) When $c > 1$, determine the range of values of $\theta$ that correspond to the inner loop. For your answer, list the values of $\theta,$ where $0 \le \theta < 2\pi,$ at which the loop begins and ends, giving these values in increasing order. Your answer may depend on $c$.

Smaller value of $\theta$:

Larger value of $\theta$:

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(b) When $c < -1$, determine the range of values of $\theta$ that correspond to the inner loop. For your answer, list the values of $\theta,$ where $0 \le \theta < 2\pi,$ at which the loop begins and ends, giving these values in increasing order. Your answer may depend on $c$.

Smaller value of $\theta$:

Larger value of $\theta$: