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Since the difference between maximum and minimum is 8, the amplitude is 4.
Since the local maximum is at -pi/3, you add pi/3 to the x value.
Since the difference in the x value of the maximum and minimum is pi, the period is 2pi.
Since the average between the maximum and minimum is -3, you add 3 to the y value.
This leaves you with the equation y = 4cos(x+pi/3) - 3
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