How many degrees of rotation bring the point $C$ back to the position shown in Fig. 5?)\
(c) What are the values of $y(t)$ at the points where $y(t)$ has zero slope?\
(d) Suppose that $x(t)=R \cos (pt)$. What are the values of $x(t)$ at the points where $y(t)$ has zero slope?\
(e) What are the values of $y(t)$ at the points where $x(t)$ has zero slope?\
(f) From the fact that $\cos (\theta) = \sin 
(\theta + 90^{\circ})$, what can you say about the [*shape*]{} of the graph of $x(t)$? (Hint: could you match the graphs of $x(t)$ and $y(t)$ by sliding one over the other?)\
(g) Sketch the derivative of the curve shown in Fig. 3. Where the curve is increasing, the derivative is positive, the faster the increase then the more positive the derivative; correspondingly for places where the curve is decreasing. Compare your curve with the cosine curve of part (f). Redo your sketch after you have finished this subsection.

The functions $x(t)$ and $y(t)$ in the last exercise keep repeating themselves as $t$ increases. The repetitious behavior is not surprising, because it is connected with the motion of a point that is moving around the 