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.