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