Write a general formula for finding the height of the rider during this time interval in the form of a sinusoidal function: h(t) = A sin(Bt-C) + D
Write a general formula for finding the height of the rider during this time interval in the form of a sinusoidal function: h(t) = A sin(Bt-C) + D
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section: Chapter Questions
Problem 75RE
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Transcribed Image Text:macy Hufford
More Ferris Wheel
In the previous Ferris Wheel activity, you found Carlos's height at different positions on the Ferris wheel using
right triangles, as illustrated in the diagram.
Recall the following facts from the previous lesson:
The Ferris wheel has a radius of 25 feet.
The center of the Ferris wheel is 30 feet above the ground.
Carlos has also been carefully timing the rotation of the wheel and has observed the following additional fact:
The Ferris wheel makes one complete revolution counterclockwise every 20 seconds.
538 D
.
.
41.7 E
30 F
15.3 G
612
Elapsed time
since passing
position A
1 second
2 seconds
3 seconds
с
1. Calculate the height of a rider at each of the following times t, where t represents the number of
seconds since the rider passed position A on the diagram. Keep track of any regularities you notice in
the ways you calculate the height. As you calculate each height, plot the position on the Ferris wheel
provided.
8 seconds
844.7 h(t)=25sin (18t)+30=441
(25Ft-Sin 36)+30
= 44.6946
25 sin(36)
A 300, 20
14.5 seconds.
J15.3
6.2
Height of the
Rider
Sin19=X+30
25
37.7
25936+30
44.7
6 seconds 259in72+ 30
53.7764
7.5 seconds 44.7
Sin54 +30
502 25
25 sin36+30
44.6946
Elapsed time since
passing position A
5. sin(21) = cos(t)
18 seconds
23 seconds
28 seconds
36 seconds
40 seconds
Height of the rider
-25 Sin 36+30
= 15.3054
25 Sin36 +30=
44.6946
-25 Sin 72+30
=6.2236
30
Transcribed Image Text:4.
3.
2. Draw a graph of the height of the rider with respect to the elapsed time since passing position A
Find the properties of the sinusoidal graph above:
Amplitude, A =
Midline, D =
Period, P =
Phase shift C/B =
value of B =
value of C =
t
Write a general formula for finding the height of the rider during this time interval in the form of a
sinusoidal function:
h(t) = A sin(Bt-C) + D
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