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Graph the curves having the following polar equations. (a) r² = sin(20). Explain how the curve relates to the lemniscate of Bernoulli. (b) r = sin 30 and r = sin(40). Explain why the number of "petals" in the two curves are so different. (c) r = 1 + cos ("cardioid") and r= 1 + 2 cos() ("limaçon") Discuss the similar- ities and differences of the curves. For what values of 0 does the limaçon intersect itself?

Graph the curves having the following polar equations. (a) r² = sin(20). Explain how the curve relates to the lemniscate of Bernoulli. (b) r = sin 30 and r = sin(40). Explain why the number of "petals" in the two curves are so different. (c) r = 1 + cos ("cardioid") and r= 1 + 2 cos() ("limaçon") Discuss the similar- ities and differences of the curves. For what values of 0 does the limaçon intersect itself?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Graph the curves having the following polar equations. (a) r² = sin(20). Explain how the curve relates to the lemniscate of Bernoulli. (b) r = sin 30 and r = sin(40). Explain why the number of "petals" in the two curves are so different. (c) r = 1 + cos ("cardioid") and r = 1+2 cos(0) ("limaçon") Discuss the similar- ities and differences of the curves. For what values of does the limaçon intersect itself?
Transcribed Image Text:Graph the curves having the following polar equations. (a) r² = sin(20). Explain how the curve relates to the lemniscate of Bernoulli. (b) r = sin 30 and r = sin(40). Explain why the number of "petals" in the two curves are so different. (c) r = 1 + cos ("cardioid") and r = 1+2 cos(0) ("limaçon") Discuss the similar- ities and differences of the curves. For what values of does the limaçon intersect itself?
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