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34. (a) Find a parametric representation for the torus obtained by rotating about the z-axis the circle in the xz-plane with center (b, 0, 0) and radius a

34. (a) Find a parametric representation for the torus obtained by rotating about the z-axis the circle in the xz-plane with center (b, 0, 0) and radius a

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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I would need some help with this problem #34, please?

CHAPTER 10 REVIEW 733 33. (a) What happens to the spiral tube in Example 2 (see Fig- ure 5) if we replace cos u by sin u and sin u by cos u? (b) What happens if we replace cos u by cos 2u and sin u by sin 2u? (х, у, z) 34.)(a) Find a parametric representation for the torus obtained by rotating about the z-axis the circle in the xz-plane with center (b, 0, 0) and radius a < b. [Hint: Take as param- eters the angles 0 and a shown in the figure.] (b) Use the parametric equations found in part (a) to graph y the torus for several values of a and b. (b, 0, 0)
Transcribed Image Text:CHAPTER 10 REVIEW 733 33. (a) What happens to the spiral tube in Example 2 (see Fig- ure 5) if we replace cos u by sin u and sin u by cos u? (b) What happens if we replace cos u by cos 2u and sin u by sin 2u? (х, у, z) 34.)(a) Find a parametric representation for the torus obtained by rotating about the z-axis the circle in the xz-plane with center (b, 0, 0) and radius a < b. [Hint: Take as param- eters the angles 0 and a shown in the figure.] (b) Use the parametric equations found in part (a) to graph y the torus for several values of a and b. (b, 0, 0)
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