Question

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 pi?

Answer 1

The cosine function with the given characteristics is:

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

How to get the cosine function?

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:

brainly.com/question/4372174

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