The cosine function will be equal to f(x) = 3cos(π(6/7)x) + 4
What is a function?
A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
A generic cosine function is written as:
f(x) = Acos(wx + p) + M
where:
A = amplitude
w = angular frequency
p = phase
M = midline.
We know that:
The midline is 4, then M = 4
The amplitude is 3, then A = 3
There is no information about the phase, so p = 0.
And we know that the period is 7/3.
The period is written as T, and the relation between the period and the angular frequency is:
T = 2π/w
Then we have:
7/3 = 2π/w
w = (2π)*(3/7) = π x (6/7)
where π= 3.14
Then we have:
w = π x (6/7)
A = 3
M = 4
p = 0
Then the cosine function is: f(x) = 3cos(π(6/7)x) + 4
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