SOLUTION: Determine an equation for a cosine function with adjacent maximum at (60°, 5) and minimum at (150°, 1). I need your help asap!

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Question 1181068: Determine an equation for a cosine function with adjacent maximum at (60°, 5) and minimum at (150°, 1).
I need your help asap!

Answer by greenestamps(13215)   (Show Source): You can put this solution on YOUR website!


Allow me to work with radian measures, which is easier....

maximum at (pi/3,5) and adjacent minimum at (5pi/6,1)

f(x) = a*cos(b(x-c))+d

a is the amplitude
b determines the period (the period is 2pi/b)
c is the horizontal shift
d is the vertical shift

The maximum and minimum values are 5 and 1. That makes the center line at y=3 and the amplitude 2:
a=2; d=3

From a maximum to the adjacent minimum is half a period. That difference in this example is pi/2, so the period is pi. So 2pi/b = pi, which means
b=2

The maximum of the basic cosine function is at x=0; in this example the maximum is at 60 degrees, or pi/3. So the horizontal shift is pi/3.
c = pi/3

The function (using radian measure) is



A graph showing the function from -pi/2 to +pi:
maximum value 5 at 60 degrees = pi/3 radians or about 1.05; minimum value 1 at 150 degrees = 5pi/6 radians or about 2.62




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