sentences what your graph would look like if it showed $Y$-values for many revolutions of the wheel.\

The last exercise demonstrates that the vertical position of the point $C$ in Fig. 5 can be written as a function of time (assuming that the sprocket rotates with constant speed) as $$Y(t) =R\sin (pt)
\label{eq:Y(t)7}$$ where $p$ is the rotational speed of the sprocket and $R$ is the radius of the circle described by the pedal. Similarly the horizontal position of $C$ would be written as $$Y(t) =R\cos (pt)
\label{eq:X(t)7}$$ The vertical positions of the pedals in Fig. 3 would be equal to $Y(t)$, as Fig. 4 indicates.\
Let’s get more familiar with the sine function.

[**EXERCISE**]{}

[**3.2**]{}\
Suppose that a function $y(t)=R \sin (pt)$, where R and p are constants. You may use Fig. 4 as a graph of $y(t)$.\
(a) Suppose that $pt$ is equal to some fixed number $\theta$ that lies between $0^{\circ}$ and $360^{\circ}$. How often will $y(t)$ repeat the same value of $y$ as $t$ increases forever?\
(b) How many degrees separate the points on a graph of $y(t)$ as a function of $pt$ where y(t) not only has the same value, but has positive slope? (Hint: 