Jade is having a wonderful time riding a merry-go-round. Her distance $d$ (in feet) from the fence nearest the entrance is given by the equation $d = 25 \operatorname { sin } ( \frac { \pi t } { 15 } ) + 35$ where $t$ is the time in seconds since the merry-go-round started to rotate.

1. How close can Jade be to the fence? How far?

   Hint (a):

   What are the minimum and maximum values of the function?

2. How long does it take for the merry-go-round to complete one revolution?

   Hint (b):

   This is the time for one cycle, or the period. You are given the frequency.
   $\left(\text{frequency}\right)\left(\text{period}\right) = 2π$

3. How long before Jade is $60$ feet from the fence for the second time?

   Hint (c):

   $f\left(t\right) = 60$
   Find $t$.

4. Sketch the graph of $d$ vs. $t$. Label and scale (put numbers on) the axes appropriately.

   Graph: