(a) In Example 11 the graphs suggest that the limaon r 1 c sin has an inner loop when c 1 Prove that this is true, and find the values of that correspond to the inner loop (b) From Figure 18 it appears that the limaon loses its dimple when c Prove this ...

a We see that the curve crosses itself at the origin where r 0 in fact the inner ...

(a) In Example 11 the graphs suggest that the limaon r = 1 + c sin has...

Question:

(a) In Example 11 the graphs suggest that the limaçon r = 1 + c sin θ has an inner loop when | c | > 1. Prove that this is true, and find the values of θ that correspond to the inner loop.
(b) From Figure 18 it appears that the limaçon loses its dimple when c = ½. Prove this.