Section 3.7 Sinusoidal Functions as Mathematical Models

Suppose that the waterwheel pictured rotates at 6 revolutions per minute (rpm). Two seconds after you start a stopwatch, point P on the rim of the wheel is at its greatest height, d = 13 ft, above the surface of the water. The center of the waterwheel is 6 ft above the surface.

Sketch the graph of d as a function of t, in seconds, since you started the stopwatch.

Assuming that d is a sinusoidal function of t, write a particular equation.

How high above or below the water’s surface will P be at time t = 17.5 sec? At that time, will it be going up or down? d = -0.7 ft, going up

At what time t was point P first emerging from the water? t = 7.8611 sec