MELT Algebra and Functions: Trigonometric Functions
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25 Feet
30 Feet
1. You and a group of friends want to ride the Ferris wheel at the local county fair.
Your friend Anna wants to know how high she will be at the top of the Ferris
Wheel? What about midway up or midway down? What about at the bottom of
the wheel?
Created by Sumer Inman
Adapted from Mathematics Vision Project Secondary Mathematics III, Module 6
MELT Algebra and Functions: Trigonometric Functions
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2. Having just finished a trigonometric ratio unit at school you begin to wonder
about the height at each spoke of the wheel. Find the height at each point (A-J)
on the Ferris wheel.
3. Doing an internet search Anna finds an equation h(t)= 30+ 25sin(θ). It gives the
right answers for the height at any point on the Ferris wheel even when the
reference angle is greater than 90 degrees. Anna doesn’t understand why this
equation works because right trigonometry is only defined for acute angles.
Explain to Anna why this equation works.
You notice that the Ferris wheel makes a complete counter-clock rotation every 20
seconds.
4. Using this information calculate the height of a rider at each of the following
times t, where t represents the number of seconds since the rider passes position
A on the diagram. Keep track of any regularities you notice in the ways you
calculate the height.
Elapsed time
since passing
position A
Calculations
Height of the
rider
0 sec
1 sec
1.5 sec
2 sec
2.5 sec
3 sec
5 sec
6 sec
8 sec
9 sec
10 sec
Created by Sumer Inman
Adapted from Mathematics Vision Project Secondary Mathematics III, Module 6
MELT Algebra and Functions: Trigonometric Functions
Page |3
12 sec
14 sec
15 sec
18 sec
19 sec
20 sec
23 sec
28 sec
35 sec
36 sec
37 sec
40 sec
5. Based on the above data, sketch a graph of the height of a rider on this Ferris
wheel as a function of the times elapsed since the rider passed the position
farthest to the right on the Ferris wheel. (We can consider this position as the
rider’s starting position at time t=0.)
6. Write an equation of the graph you sketched in above question.
7. How would your graph change if:
 The radius of the wheel was larger or smaller?
 The height of the center of the wheel was greater or smaller?
Created by Sumer Inman
Adapted from Mathematics Vision Project Secondary Mathematics III, Module 6
MELT Algebra and Functions: Trigonometric Functions

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The wheel rotates faster or slower?
8. How would your equation change if:
 The radius of the wheel was larger or smaller?
 The height of the center of the wheel was greater or smaller?
 The wheel rotates faster or slower?
Once on the ride you and your friends start to notice the shadow you cast on the
ground. To describe the location of your shadow we could measure the shadow’s
horizontal distance to the right and left of the point directly beneath the center of the
Ferris wheel.
9. Calculate the location of your shadow at the times t given the following table,
where t represents the number of seconds since you passed the position farthest
to the right on the Ferris wheel. Keep track of any regularities you notice in the
ways you calculate the location of the shadow.
Elapsed time
since passing
position A
Calculations
Height of the
rider
0 sec
1 sec
1.5 sec
2 sec
2.5 sec
3 sec
5 sec
6 sec
8 sec
9 sec
10 sec
12 sec
14 sec
15 sec
18 sec
19 sec
20 sec
23 sec
Created by Sumer Inman
Adapted from Mathematics Vision Project Secondary Mathematics III, Module 6
MELT Algebra and Functions: Trigonometric Functions
Page |5
28 sec
35 sec
36 sec
37 sec
40 sec
10. Based what you did in #9, sketch a graph of the horizontal location of your
shadow as a function of the time t, where t represents the elapsed time after you
pass position A.
11. Write a general formula for finding the location of the shadow at any instant in
time.
Created by Sumer Inman
Adapted from Mathematics Vision Project Secondary Mathematics III, Module 6
MELT Algebra and Functions: Trigonometric Functions
Created by Sumer Inman
Adapted from Mathematics Vision Project Secondary Mathematics III, Module 6
Page |6
MELT Algebra and Functions: Trigonometric Functions
Created by Sumer Inman
Adapted from Mathematics Vision Project Secondary Mathematics III, Module 6
Page |7
MELT Algebra and Functions: Trigonometric Functions
Created by Sumer Inman
Adapted from Mathematics Vision Project Secondary Mathematics III, Module 6
Page |8
MELT Algebra and Functions: Trigonometric Functions
Created by Sumer Inman
Adapted from Mathematics Vision Project Secondary Mathematics III, Module 6
Page |9
MELT Algebra and Functions: Trigonometric Functions
Created by Sumer Inman
Adapted from Mathematics Vision Project Secondary Mathematics III, Module 6
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