The parent functions of sine and cosine functions are and respectively. Thus, it is important to know how their graphs look and some of their characteristics. Graphing them is done by first evaluating some inputs and obtaining their corresponding outputs using a table. Here, radians will be used, but the functions can be evaluated for degrees as well.
Plotting these points and connecting them with smooth curves gives the graphs.
Amplitude = ∣a∣ Period =
The graph shows the function
Using the graph, find the amplitude and period of the function. Then, verify them using the rule.
We can find the amplitude of the function by reading the greatest and least function values and calculating half the difference between them. From the graph, it can be seen that the greatest value is 1.5 and the least is -1.5.
As the points intersecting the midline correspond to the x-intercepts of the parent function, the midline should be the first thing graphed. Here, the midline is y=1.
The graph can now be drawn through the plotted points, continuing periodically in both directions.
Using the function rule, answer the following questions.
Realistically, the ride should start at the same height as the entry. That is, when t=0. Therefore, substituting t=0 into the function gives us the height of the entry.
As the angle -0.5π is equal to it corresponds to the coordinate (0,-1) on the unit circle. Thus, is equal to -1.
We can now conclude that the entry to the ferris wheel is 4 feet off ground level.