$X$ and $Y$, shown in the figure, in terms of the sine and cosine of the angle $\theta$. (Hint: if you have trouble with this part, review the sine and cosine definitions in one of your old math books - or a dictionary.)\
(b) Make a graph of the length $Y$ as a function of the angle $\theta$, using $\theta$ intervals of $10^{\circ}$ between $0$ and $360^{\circ}$. Does your graph resemble a portion of Fig. 4? Be sure to plot the $Y$ values on the vertical axis.\

![image](fig5.eps)

\(c) Suppose the point $C$ in the figure moves around the circumference of the circle with constant speed so that $\theta = pt$, $t$ being the time. Can you now make a graph of the length $Y$ as a function of the time? (Hint: Can you save yourself a lot of work be just relabeling the x-axis of your previous figure? Does it help to use time units of $\frac{degrees}{p}$, even though you don’t have a numerical value for $p$?\
(d) Now sketch, without calculating, the graph of $Y$ for one more complete revolution of the point $C$ around the wheel. Compare your graph with Fig. 3. Explain in one or two 