The limaon family The equations r = a + b cos u and r = a

Chapter 10, Problem 89

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The limaon family The equations r = a + b cos u and r = a + b sin u describe curves known as limaons (from Latin for snail). We have already encountered cardioids, which occur when _ a _ = _ b _. The limaon has an inner loop if _ a _ 6 _ b _. The limaon has a dent or dimple if _ b _ 6 _ a _ 6 2_ b _. And the limaon is oval-shaped if _ a _ 7 2_ b _. Match equations af with the limaons in the figures AF. a. r = -1 + sin u b. r = -1 + 2 cos u c. r = 2 + sin u d. r = 1 - 2 cos u e. r = 1 + 2 sin u f. r = 1 + 23 sin u 9