The revolution of a sinusoid describes the three-dimensional surface created when a sine wave is rotated around a fixed axis, usually the horizontal axis on which the wave lies. As the curve revolves, each point sweeps out a circle, turning the familiar up-and-down motion of the sine function into a smooth, wavelike surface. Where the sine wave reaches its maximum and minimum, the surface becomes widest, and where the curve crosses the axis, the surface narrows to a thin point. This repeating pa