Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question

The limaçon family The equations r = a + b cos θ and r = a + b sin θ describe curves known as limaçons (from Latin for snail). We have already encountered cardioids, which occur when | a | = | b | . The limaçon has an inner loop if | a | < | b | . The limaçon has a dent or dimple if 
| b | < | a | < 2 | b | . And the limaçon is oval-shaped if | a | > 2 | b | . Match equations a–f with the limaçons in figures A–F.

a. r = -1 + sin θ              b. r = -1 + 2 cos θ
c. r = 2 + sin θ               d. r = 1 - 2 cos θ
e. r = 1 + 2 sin θ            f. r = 1 + 2/3 sin θ

y 4 y. 3+ (А) (В) y -2+ (С) (D) yA 2 -1+ -2 (E) (F)
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Transcribed Image Text:y 4 y. 3+ (А) (В) y -2+ (С) (D) yA 2 -1+ -2 (E) (F)
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