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Math Help - parameric equations

  1. #1
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    parameric equations

    x=2-3cos(t)
    y=1+2sin(t)

    a)it asks for all points for vertical and horizontal tangency, which im not sure we covered in class or i dont understand it

    b) eliminate the parameter

    c) setup integral for area of surface by generated by revolving around line y=1.

    these three questions, i am complety lost , any help will be greatly appreciated
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  2. #2
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    Quote Originally Posted by twofortwo View Post
    x=2-3cos(t)
    y=1+2sin(t)

    a)it asks for all points for vertical and horizontal tangency, which im not sure we covered in class or i dont understand it

    vertical ... dy/dx = (dy/dt)/(dx/dt) is undefined.

    horizontal ... dy/dx = (dy/dt)/(dx/dt) = 0.

    b) eliminate the parameter

    cos(t) = (2-x)/3

    sin(t) = (y-1)/2

    now use the fact that sin^2(t) + cos^2(t) = 1


    cartesian equation will be an ellipse

    c) setup integral for area of surface by generated by revolving around line y=1.

    have to think about this one
    ...
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  3. #3
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    Quote Originally Posted by skeeter View Post
    ...
    what number are you pluggin into the derivitive to get an undefined tangency and zero tangency...

    thanx
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  4. #4
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    Quote Originally Posted by twofortwo View Post
    what number are you pluggin into the derivitive to get an undefined tangency and zero tangency...

    thanx
    you have to solve for t

    vertical ... dx/dt = 0

    horizontal ... dy/dt = 0
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  5. #5
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    Quote Originally Posted by twofortwo View Post
    x=2-3cos(t)
    y=1+2sin(t)

    c) setup integral for area of surface by generated by revolving around line y=1.
    rotating the ellipse ...

    x = 3\cos{t}

    y = 2\sin{t}

    about the x-axis (y = 0) will yield the same result.

    might be easier to work.
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  6. #6
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    if i solve dx/dt=3sint t for t, i get 0 and pi
    and if i solve dy/dt for t, i get pi/2 and 3pi/2

    my answers arent matching up with yours and im so sorry to keep peestering yu about the same problem but im honestly not getting it.
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  7. #7
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    Quote Originally Posted by twofortwo View Post

    points on the curve are (x,y) evaluated at those values of t ...

    if i solve dx/dt=3sint t for t, i get 0 and pi

    x(0) = ?
    x(pi) = ?

    and if i solve dy/dt for t, i get pi/2 and 3pi/2

    y(pi/2) = ?
    y(3pi/2) = ?
    ...
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