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?
- kbLv 78 years agoFavorite 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!