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Math Help - line rotation at certain points

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by dat1611 View Post


    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?
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  3. #3
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    im not sure what do with the g(x) and f(x)
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