Florence the Cricket was trying to cross a road. A clown on a unicycle overtook her and Florence got caught in the tread of the tire. Florence's height from the pavement then began to vary sinusoidally with the distance the unicycle travels. a) If the diameter of the tire is 36 inches, draw a graph that shows the height, h in inches, of Florence from the road in terms the distance, d in inches the unicycle travels, from the point where Florence got lodged in the tread. Keep d in terms of π. Reminder: C 2πr. Clearly show your scale on both the x and y axis and draw at least on cycle.

b) Write a cosine equation equation that models your graph above.

c) Determine how high off the pavement Florence is after the unicycle has gone exactly 1/4 mile. (Reminder: 1 mile = 5280 feet).

Show or explain your reasoning.

d) If the unicycle is traveling at 11 mph, what is Florence's angular speed in radians per hour?