Math 30-1
5.1 – 5.4 Graphing Trigonometric Functions Task
Warm Up: Graph two cycles for each function equation and determine the characteristics.


1. y  2sin  3    1
2

Amplitude:
Displacement:
Zeros:
Period:
Domain:
y-intercept:
Phase Shift:
Range:
Period:
Domain:
y-intercept
Phase Shift:
Range:
2. y  4cos(  30 )  2
Amplitude:
Displacement:
Zeros:
3. y  tan 
Asymptotes:
Zeros:
Domain:
Period:
y - intercept
Range:
4. Write an expression for the range of the graph of the function y  3sin   7 .
5. Write a cosine function to model the graph.
(x-axis is in degrees)
6. Write a sine function to model the graph.
(x-axis is in degrees)
Ferris Wheel Comparison Project
The 1893 Chicago World’s Fair is considered the birthplace of the classic amusement park ride,
the Ferris wheel. The architectural wonder was created by an American engineer named George
Ferris. The original Ferris wheel no longer exists. But, in 1990, a new Ferris wheel was built at
Navy Pier in Chicago to resemble the original. While the Navy Pier Ferris Wheel is a beautiful
Chicago landmark, its grandeur actually pales in comparison to Mr. Ferris’ creation.
The Ferris wheel built for the World’s Fair had a diameter of 250 feet. It stood 14 feet off the
ground. It had 36 wooden boxcars that were the size of train cars. Each car could hold 60
people! The wheel would load cars in such a way that each rider could enjoy a full rotation that
lasted about 10 minutes.
The Ferris wheel at Navy Pier has a diameter of 140 feet. It stands 10 feet off the ground. The
wheel has 40 gondolas that seat six passengers each. It takes about 6 minutes for the Navy Pier
Ferris Wheel to complete one rotation.
Below is a picture of the first Ferris wheel next to the Ferris wheel at Navy Pier.
In the space below is a diagram of the World’s Fair Ferris wheel and the boarding platform.
Fill in the necessary information. Let h represent the vertical position (height) at time t, where t
is given in minutes. Determine the height for five critical times.
Before you sketch the graph of the function that models the height of a car over time for the
Ferris wheel, determine each of the following.
1. What is the label for the x-axis?
2. What is the label for the y-axis?
3. Is the angle measured in degrees or radians?
4. What is the amplitude of the graph?
a = __________
5. What is the period of one cycle of the curve?
The value of b is _________
6. What are the maximum and minimum values of the curve? Max _____ Min ________
displacement = __________
7. What is the height at time = 0? ______. What characteristic of the graph does this
represent?
Sketch the graph that models one revolution of the Ferris wheel. Label the axes.
8. Write a cosine function that models the path of the car in the form y  a cos(b( x  c))  d
.
9. Write a sine function that models the path of the car in the form y  a sin(b( x  c))  d .
10. If you begin your ride at the base of the wheel, what is your height after each time?
a) 1 minute
b) 4 minutes
11. At what time(s), to the nearest tenth of a minute, will you reach the following heights?
a) 100 ft.
b) 240 ft.
Consider the Navy Pier Ferris Wheel.
In the space below is a diagram of the Navy Pier Fair Ferris Wheel and the boarding platform.
Fill in the necessary information. Let h represent the vertical position (height) at time t, where t
is given in minutes. Determine the height for five critical times.
Sketch and label the graph that models one revolution of the Navy Pier Ferris wheel.
1. Write a cosine function that models the path of the car in the form y  a cos(b( x  c))  d
.
2. Write a sine function that models the path of the car in the form y  a sin(b( x  c))  d .
3. At what speed is the wheel traveling in feet/second?
4. If you begin your ride at the base of the wheel, what is your height after each time
period?
a)1 minute
b) 4 minutes
5. At what time(s), to the nearest tenth of a minute will you reach the following heights?
a.) 100 ft.
b.) 240 ft.
Ferris Wheel Extension
1. Imagine the Navy Pier and the Worlds Fair Ferris Wheel being built beside each other. If
both wheels begin turning at once, over a 20 minute time period, at what times are the
wheels at the same height?
2. What is the length of the arc traveled by the Navy Pier Ferris wheel from the
4 o’clock to the 7 o’clock position?