APPLICATIONS OF SINUSOIDAL FUNCTIONS
1. Bill is riding on a Ferris wheel. His height above the ground in metres with
respect to time in seconds is represented by the following graph.
a. Write the equation of the sinusoidal function, first as a transformation
of y = sin x, and then as a transformation of y = cos x.
b. Use either equation from part (a) to determine whether or not Bill would
be able to get off the Ferris wheel safely after 38 s.
2. Sarah is sitting in an inner-tube in a wave pool. Her height above the bottom
of the pool varies sinusoidally with time. At time t = 2 seconds Sarah is at the
top of a wave, 3.5 m from the bottom of the pool. At t = 4 seconds she is at
the bottom of the wave, 2.5 m from the bottom of the pool.
a. Mark appropriate scales on the axes below and sketch a graph that
represents Sarah’s height above the bottom of the pool as a function of
time. Show two complete periods.
b. Write an equation that describes the graph in part (a).
c. Use the equation from part (b) to determine Sarah’s height above the
bottom of the pool at time t = 12.5 seconds.
3. A water wheel with diameter 8 m takes 16 minutes for 1 revolution. As the
wheel begins to turn, a nail on its rim is at the lowest point, 1 m below the
water surface.
a. Mark appropriate scales on the axes below and sketch a graph that
represents the height of the nail above (or below) water level during two
revolutions of the wheel.
b. Write an equation that describes the graph in part (a).
c. Use the equation from part (b) to determine the nail’s height after
25 minutes.