Graphing A Sine Wave:

Assume that you draw an accurate graph of the swinging object's location with respect to time as view from edge-on. The time is plotted horizontally; the past is in the direction of the left, and the future is in the direction of the right. One complete revolution of the object emerges on the graph as a sine wave. The degree values can be assigned all along this wave corresponding to the degrees around the circle as shown in figure below.

Figure: Graphic symbolization of a sine wave as circular motion.

Constant rotational motion, like that of the object on the string, occurs all over the universe. The child rotating the object ca not make the object unexpectedly slow down and speed up, or immediately stop and change direction, or rotate in steps like a ratchet wheel. Though, once that mass is moving, it does not take much energy to continue it going. The uniform circular motion is a theoretical ideal. There is no enhanced way to whirl an object around and around. The sinusoid is a theoretical ideal, also. There is no improved way to make a wave.