by introducing that viewpoint. “Spheriod trigonometry”, however, can safely be left for a later course.

Circular Motion
---------------

The sine and cosine can be used in the description

![image](fig3.eps)

of circular motion. Look, for example, at Fig 3 which is a close-up view of the working part of a bicycle. The bicycle moves forward as the rear wheel is forced to rotate by the chain, which is driven by the rotation of the sprocket. But the sprocket is made to rotate by the up-and-down motion of the bicyclist’s feet.

![image](fig4.eps)

Fig 4 is a graph that plots the vertical position of the bicyclist’s left foot against time, assuming that the bicyclist rotates the sprocket with constant speed. The vertical scale shows the height of the bicyclist’s left foot above or below the position shown in Fig. 3, which is taken to be at zero time.

The curve shown in Fig. 4 represents the sine function that you learned about in connection with right triangles. Its connection with circular motion should become clear after the next exercise.

[**EXERCISE**]{}

[**3.1**]{}\
(a) The circle shown in Fig. 5 has a radius that is exactly equal to one unit of length. Express the distances 