Question 1100458: Unit: Trigonometric functions (Graphs of sine, cosine, and tangent functions)
The Octopus ride at an amusement park completes one revolution every 60 s. The cars reach a max of 4m above the ground and a minimum of 1m above the ground. The height, h, in meters, above the ground, can be modeled using a sine function of the form h = asin(kt) + c, where t represents the time, in seconds.
a)determine the amplitude of the function?
b) determine the vertical translation of the function
c) what is the desired period of the function? (I got this and it's 60 seconds)
d) determine the value of k that results in the period desired in part c.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Part A
To find the amplitude, first find the vertical distance from the highest point to the lowest point. This distance is 3 (since 4-1 = 3, where 1 represents the lowest point and 4 is the highest point).
Cut this value in half to get 3/2 = 1.5
Therefore the amplitude is 1.5
This is the distance from the vertical center point to either the peak point or the lowest point.
Side Note: this is the value of 'a' in the equation h = a*sin(kt) + c
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Part B
Find the midpoint of 1 and 4 to get (1+4)/2 = 5/2 = 2.5
The vertical translation is therefore 2.5 meaning that the center part of the ride is 2.5 meters above the ground.
Side Note: this is the value of 'c' in the equation h = a*sin(kt) + c
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Part C
You are correct. Nice work.
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Part D
From part C, the period is 60 seconds.
T = period
T = 60
We'll use this value of T to find the value of k
T = 2pi/k
60 = 2pi/k
60k = 2pi
k = 2pi/60
k = pi/30
This is assuming you want the value of k in radians.
If you want it in degrees, then multiply pi/30 by the conversion factor 180/pi to get (pi/30)*(180/pi) = 6
So k = pi/30 if you are in radian mode, or k = 6 if you are in degree mode.
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