Question 1134825: Complete the chart and find equations describing the trig function:
X values: 4, 4.9, 5.8, 6.7, 7.6
Y values: 13, 4.5, -4, 4.5, 13
A:
B:
C:
D:
Write in form y=d+acos(b(x-c))
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
The function has a maximum value of 13 at x=4 and again at x=7.6, so the period is 7.6-4 = 3.6.
The function has a minimum value of -4 halfway through the period, at x=5.8. So the oscillation is between -4 and 13; that makes the amplitude 8.5 and the centerline 4.5.
The basic cosine graph has its maximum at 0; since this function has its "first" maximum at x=4, the phase shift is 4.
In the equation
a is the amplitude, c is the phase shift, and d is the vertical shift.
At this point we know a=8.5, c=4, and d=4.5; we need to determine b, which determines the period.
The value of b, to get the length of the period equal to 3.6, is
b = (2pi)/3.6
So the complete function is
Here is a graph, with horizontal lines showing the maximum and minimum values and the centerline of the function.
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