A clock with an hour hand that is 15 inches long is hanging on a wall. At noon, the distance between the tip of the hour hand and the floor is 96 inches. At 3p. m., the distance is 86 inches;
at 6 p. m., 76 inches, at 9 p. m., 86 inches; and at midnight, the distance is again at 96 inches. If y
represents the distance between the tip of the hour hand and the ceiling x hours after noon, write
a sinusoidal function to model the relationship between these two variable quantities.