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Pre – Calculus Math 40S: Explained!
www.math40s.com
76
Trigonometry Lesson 8:
Part I
–
Ferris Wheels
One of the most common application questions for graphing trigonometric functions involves Ferris wheels,
since the up and down motion of a rider follows the shape of a sine or cosine graph.
Example:
A Ferris wheel has a diameter of 30 m, with the centre
18 m above the ground. It makes one complete rotation every 60 s.
a)
Draw the graph of one complete cycle, assuming
the rider starts at the lowest point.
b)
Find the cosine equation of the graph.
c)
What is the height of the rider at 52 seconds?
10
20
30
40
50
60
5
10
a.
When you look at a Ferris wheel it
makes a circular motion. Do NOT
draw
a circle as your graph. The graph
represents the up & down motion over
time.
In the first half of
the graph, we can see the person will
go up from 3 m to 33 m in 30 seconds.
In the second half, the person will go
back down to 3 m.
d)
At what time(s) is the rider at 20 m?

35
15
20
25
30
Midline at 18 m
Height (m)
avalue:
We know the diameter of the
wheel is 30 m, so the radius (which is
the same as amplitude) will be 15 m.
bvalue:
The period is 60 s, so:
b.
Time (s)
c.
Method 1:
Plug 52 s in for
time in either the cosine
equation. Simplify and
calculate with your TI83 in
radian mode
( )
15cos
18
30
(52)
15cos
52
18
30
(52)
7.96 m
h t
t
h
h
π
π
= −
+
= −
+
=
Method 2:
Put your
calculator in radian mode
and graph either the
cosine function.
2
nd
Trace
Æ
Value
Æ
x = 52
This will calculate the
height directly from the
graph.
2
2
60
30
b
P
π
π
π
=
=
=
cvalue:
There is none in the cosine
pattern.
dvalue:
The centre of the wheel is 18
m above the ground, so that will be the
midline
The cosine pattern is upside down,
so you need to put a negative in front.
h(t)= 15cos
t+18
30
π
d.
To find the times the rider is at 20 m, graph a horizontal line in
your TI83 at y = 20, then find the points of intersection.
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 Winter '10
 KISCABEAN
 Trigonometry, Periodic function, Ferris wheels, Calculus Math 40S

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