Consider the blue vertical line shown above (click on graph for better view) con

Question

Consider the blue vertical line shown above (click on graph for better view) connecting the graphs y=g(x)=sin(2x) and y=f(x)=cos(3x).
Referring to this blue line, match the statements below about rotating this line with the corresponding statements about the result obtained.

1. The result of rotating the line about the x-axis is
2. The result of rotating the line about the y-axis is
3. The result of rotating the line about the line y=1 is
4. The result of rotating the line about the line x=?2 is
5. The result of rotating the line about the line x=? is
6. The result of rotating the line about the line y=?2 is
7. The result of rotating the line about the line y=?
8. The result of rotating the line about the line y=??

A. a cylinder of radius x+2 and height cos(3x)?sin(2x)
B. an annulus with inner radius sin(2x) and outer radius cos(3x)
C. an annulus with inner radius ?+sin(2x) and outer radius ?+cos(3x)
D. an annulus with inner radius ??cos(3x) and outer radius ??sin(2x)
E. a cylinder of radius ??x and height cos(3x)?sin(2x)
F. a cylinder of radius x and height cos(3x)?sin(2x)
G. an annulus with inner radius 1?cos(3x) and outer radius 1?sin(2x) is
H. an annulus with inner radius 2+sin(2x) and outer radius 2+cos(3x)

Consider the blue vertical line shown above (click on graph for better view) connecting the graphs y=g(x)=sin(2x) and y=f(x)=cos(3x). Referring to this blue line, match the statements below about rotating this line with the corresponding statements about the result obtained. 1. The result of rotating the line about the x-axis is 2. The result of rotating the line about the y-axis is 3. The result of rotating the line about the line y=1 is 4. The result of rotating the line about the line x=?2 is 5. The result of rotating the line about the line x=? is 6. The result of rotating the line about the line y=?2 is 7. The result of rotating the line about the line y=? 8. The result of rotating the line about the line y=?? A. a cylinder of radius x+2 and height cos(3x)?sin(2x) B. an annulus with inner radius sin(2x) and outer radius cos(3x) C. an annulus with inner radius ?+sin(2x) and outer radius ?+cos(3x) D. an annulus with inner radius ??cos(3x) and outer radius ??sin(2x) E. a cylinder of radius ??x and height cos(3x)?sin(2x) F. a cylinder of radius x and height cos(3x)?sin(2x) G. an annulus with inner radius 1?cos(3x) and outer radius 1?sin(2x) is H. an annulus with inner radius 2+sin(2x) and outer radius 2+cos(3x)

Explanation / Answer

1. The result of rotating the line about the x-axis is

B. an annulus with inner radius sin(2x) and outer radius cos(3x)

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2. The result of rotating the line about the y-axis is

F. a cylinder of radius x and height cos(3x) - sin(2x)

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3. The result of rotating the line about the line y=1 is

G. an annulus with inner radius 1 - cos(3x) and outer radius 1 - sin(2x)

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4. The result of rotating the line about the line x=-2 is

A. a cylinder of radius x+2 and height cos(3x) - sin(2x)

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5. The result of rotating the line about the line x=pi is

E. a cylinder of radius pi - x and height cos(3x) - sin(2x)

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6. The result of rotating the line about the line y=-2 is

H. an annulus with inner radius 2+sin(2x) and outer radius 2+cos(3x)

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7. The result of rotating the line about the line y=pi

D. an annulus with inner radius pi - cos(3x) and outer radius pi - sin(2x)

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8. The result of rotating the line about the line y= - pi

C. an annulus with inner radius pi+sin(2x) and outer radius pi+cos(3x)

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