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PLANE AND SPHERICAL TRIGONOMETRY ǀ MATH 113 ǀ NOTRE DAME UNIVERSITY
FERRIS WHEEL – APPLICATION OF SINE FUNCTION-TRIGONOMETRIC FUNCTIONS

Problem # 1 : Determine the sinusoidal regression equation of the graph, to the nearest
hundredth
...
5
D = vertical displacement = y + A
y = 2 , A = 79
D = vertical displacement = 2 + 79 = 81

For B :
period = 2 π / B
from the graph, the period from start to end of the choosen part of the sine
function is between 7
...
5
...
5 – 7
...
5) ] +81  Answer

Problem # 2 : The Singapore Flyer was the largest Ferris wheel in 2011
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Steve got on the Singapore Flyer at noon
and rode it for the first time
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Questions:
2
...
b) What was Steve’s height after 25 minutes of being on the Ferris wheel
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a and 2
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As per observation, the given TABLE is a Sinusoidal Graph of Sine Function type
and has an equation of the form y = A sin [ B(x−C) ] + D where the variables has a

representation of the following:
From the graph,

A = amplitude = ( y max - y min ) / 2
y max = 541 , y min = 49
A = amplitude = ( 541 - 49 ) / 2 = 246
C = phase shift / horizontal displacement = 9
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25 and 46
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So ,
period = 46
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25 = 37
then solve for B :
37 = 2 π / B
B = 2 π / 37
So, the equation of the given graph of sine function is:

y = 246 sin [

2𝜋
37

(x−9
...

Therefore, our final Equation of Sine Function is;
h(t) = 246 sin [

2𝜋
37

(t−9
...
a ) at height=h=400ft , time=t = ?

Substitute height=h=400ft to Equation of Sine Function and then solve for t :
h(t) = 246 sin [
400 = 246 sin [

2𝜋
37
2𝜋
37

(t−9
...
25) ] + 295

400 – 295 = 246 sin [

2𝜋
37

( 400 – 295 = 246 sin [
sin [

2𝜋
37

(t−9
...
25) ] + 295

2𝜋
37

(t−9
...
25) ] =

105
246

(t−9
...
25) = 25
...
27° to Radian:
25
...
25) =

2𝜋
37

=

93499
36000

2527𝜋
18000

2527𝜋
18000

(t−9
...
25 =
t=

𝜋
180°

2527𝜋
18000

(2527)(37)

=

(18000)(2)

)

37
2𝜋

93499
36000

+ 9
...
60 + 9
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85 minutes  Answer
2
...
25) ] + 295

Substitute time=t=25minutes to Equation of Sine Function and then solve for h :
h(t) = 246 sin [
h(t) = 246 sin [
h(t) = 246 sin (

2𝜋
37
2𝜋
37

(25 −9
...
75) ] + 295

31
...
45020) + 295
h(t) = 110
...
75 ft  Answer

Brief Study Guide !
Basic Concepts:

Technical terms :
•A sinusoidal function is a function in sine or in cosine
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It is given by parameter A in function y=AsinB(x−C)+D or

y=AcosB(x−C)+D
•The period of a graph is the distance on the x axis before the function repeats itself
...

•The horizontal displacement is given by solving for x in x−C=0 in y=AsinB(x−C)+D or
y=AcosB(x−C)+D
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It is the phase shift value at x – axis with respect to origin or reference point
...
The
vertical displacement is the displacement up or down from the y axis

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