CASE STUDY: The World’s Highest Ferris wheel:
Resource Materials: “See the Views From Staten Island's Future Sky-High Wheel”
Alberts, June 11, 2015,
by Hana R.
http://ny.curbed.com/tags/new-york-wheel
http://northpolecolorado.com/explore-the-park/santas-workshop-rides/
Learning Goals: The learning goals of this case study include using trigonometric functions to
model periodic phenomena, graphing trigonometric functions, and transforming trigonometric
functions.
Warm up questions:
1. Graph the function 𝑦 = 𝑠𝑖𝑛(𝑥).
2. Graph the function 𝑦 = 𝑐𝑜𝑠 (𝑥) .
3. If 𝑓(𝑥) = 𝑠𝑖𝑛(𝑥) is the parent function, write a new function with the following
transformations:
a. f(x+2)
b. f(x)-7
c. f(3x)
d.
1
3
f(x)
4. Describe the transformations for each part of question number 3.
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See the Views From Staten Island's Future
Sky-High Wheel
Thursday, June 11, 2015, by Hana R. Alberts
By the time Staten Island's giant observation wheel finally opens in 2017, it may not be
the tallest in the world. But right now, its planned 625-foot height tops all other Ferris
wheels, and its views, unsurprisingly, have been touted as the main attraction. (Along
with the promise the project, along with its neighboring outlet mall, holds for revitalizing
St. George, the area by the Staten Island Ferry Terminal and the Staten Island
Yankees' stadium.) While we await the wheel itself, enterprising Staten Island resident
Scott Grella sent a drone up from the site to scope out the views during a particularly
lovely sunset. First, the rest of the city, while beautiful, looks mighty tiny and far away.
Second, just remember that because of FAA regulations, the drone couldn't fly all the
way up the wheel's highest point. Third, seeing these views when the wheel is actually
built will be costly as heck: $25, $35, and $45 depending on when you go, with the ticket
price escalating as the day turns into night.
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Santa’s Workshop, 5050 Pikes Peak Hwy, Cascade, CO 80809
Giant Wheel: Come ride our 60’ high ferris wheel. We must have an adult in every
car. Family Ride
Case study questions:
1. What are two possible definitions of higher? Which ferris wheel, the New York Wheel or the
Giant Wheel, is higher? Justify your reasoning.
Assume for each of the following questions that the rider enters each ferris wheel in the lowest car
which is 4 ft above the ground.
2. Write a function, g(x), that models the height above the ground of the rider on the Giant Wheel.
Let the independent variable be the angle travelled around the wheel (in radians or in degrees).
3. Write a function, f(x), that models the height above the ground of the rider on the New York
Wheel. Let the independent variable be the angle travelled around the wheel (in radians or in
degrees).
4. Graph and label both functions on graph paper using different colors for each function.
5. Write a function, h(x), that models the elevation of the rider (above sea level) on the “Giant
Wheel.” Let the independent variable be angle travelled around the wheel. Assume that the
ride’s base is at 7500 feet above sea level.
6. Write a function, k(x), that models the elevation of the rider (above sea level) on the “New York
Wheel.” Let the independent variable be the angle travelled around the wheel. Assume that the
ride’s base is 5 feet above sea level.
7. Graph and label both functions on graph paper using different colors for each function.
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Warm up questions with answers:
1. Graph the function 𝑦 = 𝑠𝑖𝑛(𝑥)
2.
Graph the function 𝑦 = 𝑐𝑜𝑠 (𝑥)
3. If 𝑓(𝑥) = 𝑠𝑖𝑛(𝑥) is the parent function, write a new function with the following
transformations:
a. f(x+2)
sin(x+2)
b. f(x)-7
sin(x) -7
c. f(3x)
sin(3x)
d.
1
3
f(x)
1
sin(x)
3
4
4. Describe the transformations for each part of question number 3
a. Left 2 units
b. Down 7 units
c. Horizontally compressed by a factor of 3
d. Vertically shrunk by a factor of 3
Case study questions with sample answers:
1. What are two possible definitions of higher? Which ferris wheel, the New York Wheel or the
Giant Wheel, is higher? Justify your reasoning.
There is higher above the ground and there is higher above sea level. Students can say
either one as long as they justify why. One is higher above the ground while the other is higher
above sea level.
Assume for each of the following questions that the rider enters each ferris wheel in the lowest car
which is 4 ft above the ground.
2. Write a function, g(x), that models the height above the ground of the rider on the Giant Wheel.
Let the independent variable be the angle travelled around the wheel (in radians or in degrees).
𝜋
𝑔(𝑥) = 28𝑠𝑖𝑛(𝑥 − 2 )+32 where x is the angle measured in radians in the counterclockwise
direction from the positive horizontal axis with origin at the center of the wheel.
3. Write a function, f(x), that models the height above the ground of the rider on the New York
Wheel. Let the independent variable be the angle travelled around the wheel (in radians or in
degrees).
𝜋
𝑔(𝑥) = 310.5𝑠𝑖𝑛(𝑥 − 2 )+314.5 where x is the angle measured in radians in the
counterclockwise direction from the positive horizontal axis with origin at the center of the
wheel.
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4. Graph and label both functions on graph paper using different colors for each function.
5. Write a function, h(x), that models the elevation of the rider (above sea level) on the “Giant
Wheel.” Let the independent variable be angle travelled around the wheel. Assume that the
ride’s base is at 7500 feet above sea level.
𝜋
ℎ(𝑥) = 28𝑠𝑖𝑛(𝑥 − 2 )+7532 where x is the angle measured in radians in the counterclockwise
direction from the positive horizontal axis with origin at the center of the wheel.
6. Write a function, k(x), that models the elevation of the rider (above sea level) on the “New York
Wheel.” Let the independent variable be the angle travelled around the wheel. Assume that the
ride’s base is 5 feet above sea level.
𝜋
𝑘(𝑥) = 310.5𝑠𝑖𝑛(𝑥 − 2 )+319.5 where x is the angle measured in radians in the
counterclockwise direction from the positive horizontal axis with origin at the center of the
wheel.
7.
Graph and label both functions on graph paper using different colors for each function.
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