What is the general equation of a cosine function with an amplitude of 3, a period of 4 pi, and a horizontal shift of negative p

Question

3 years ago

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1 answer:

liberstina [14] · Answer 1 · 2023-02-15T17:07:54+03:00

The cosine function with the given characteristics is:

f(x) = 3*cos(x/2 - pi).

<h3>How to get the cosine function?</h3>

The general cosine function is:

f(x) = A*cos(kx + p)

Where A is the amplitude and p is the phase, then we know that:

A = 3

p = -pi

Then we have:

f(x) = 3*cos(kx - pi)

And the period is equal to 4pi, then we must have that:

k*(x + 4pi) - pi = k*x - pi + 2pi

k = 1/2

Then the function is:

f(x) = 3*cos(x/2 - pi).

If you want to learn more about cosine functions:

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