Parametrization surface of revolution?

Find a parametrization for the surface of revolution: Σ is obtained by revolving about the x-axis the graph of y=cos(y) for -pi/2<_x<_pi/2

Can anyone describe to me the process?

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  • kb
    Lv 7
    8 years ago
    Favorite Answer

    The x-coordinate of the surface is the same as the x-coordinate on the curve itself, because we are revolving the curve about the x-axis.

    If v denotes the angle of rotation from the xy-plane, then the y-coordinate is shortened to y cos θ, and the z-coordinate increases to y sin θ.

    Since y = cos x, the surface can be parameterized by

    R(x, θ) = <x, (cos x) cos θ, (cos x) sin θ>.

    I hope this helps!

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