The pedal shaft on a standard bicycle is about $7$ inches long, and the center of the bottom bracket to which the pedal shaft is attached is about $11$ inches above the ground. Sketch a graph that shows the relationship of the height of the pedal above the ground as a rider pedals the bike. Assume the pedal starts in its lowest position and takes $2$ seconds to make one complete rotation.  

1. Write an equation for a function that represents your graph.

   Hint (a):

   Sketch the situation. Identify the amplitude, period, and any shifting.

2. Jack feels that the best position for the pedal to start riding is when the pedal is at $10$ inches and heading downward. What is the first time the pedal will be in this position?

   Hint (b):

   Set your equation from part (a) equal to $10$ and solve.