Question 859627: My Algebra II teacher has assigned me a long worksheet that has to do with a Ferris wheel. And I need to "Identify the amplitude, the period, the phase shift, and the center line for my curve. Write the equation of my sinusoid curve [I have never heard that word before] in terms of (i) the sine functions and (ii) the cosine function." So basically I believe I just need to find the equations. I have the data below:
X=time in seconds / Y=height in meters
0 / 5.5
10 / 10
20 / 14.5
30 / 18
40 / 19.5
50 / 18
60 / 14.5
70 / 10
80 / 5.5
90 / 2.5
100 / 1.5
110 / 2.5
Any help is beneficial for me, thank you so much for your time
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! My Algebra II teacher has assigned me a long worksheet that has to do with a Ferris wheel. And I need to "Identify the amplitude, the period, the phase shift, and the center line for my curve. Write the equation of my sinusoid curve [I have never heard that word before] in terms of (i) the sine functions and (ii) the cosine function." So basically I believe I just need to find the equations. I have the data below:
X=time in seconds / Y=height in meters
0 / 5.5
10 / 10
20 / 14.5
30 / 18
40 / 19.5
50 / 18
60 / 14.5
70 / 10
80 / 5.5
90 / 2.5
100 / 1.5
110 / 2.5
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Look for the max and min heights.
40 / 19.5 is the max
100 / 1.5 is the min
It makes 1/2 of a revolution in 60 seconds --> period = 120 seconds/revolution
Amplitude is 1/2 of the difference, (19.5 - 1.5)/2 = 9 meters
The axis of the wheel is (min + max)/2 = 10.5 meters AGL
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A sine function is
f(t) = Asin(t)
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y = f(x) = 9*sin(2pi*x/120) --> Amp of 9, and period of 120 seconds
Add 10.5
y = 9*sin(pi*x/60) + 10.5
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The sine of 0 is 0, tho, so it needs a phase shift to make it 5.5 at x=0.
9*sin((2pi*(x - 11.20415))/120) + 10.5 fits. Finding the phase shift required some interpolation.
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9*sin((2pi*(x - 11.20415))/120) + 10.5
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9*cos(90 - (2pi*x - 11.20415)/120) + 10.5
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