Thread: line rotation at certain points

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(1x).
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=π 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=π
8. The result of rotating the line about the line y=-π

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

can anyone help me match any of these

Originally Posted by dat1611

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(1x).
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=π 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=π
8. The result of rotating the line about the line y=-π

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

can anyone help me match any of these

what is your take on how they match up?

im not sure what do with the g(x) and f(x)