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? y = 4 pi cosine (3 (x minus pi)) y = 3 cosine (4 pi (x pi)) y = 3 cosine (0.5 (x pi)) y = 4 pi cosine (0.2 (x pi))

Answer 1

The general equation of a cosine function with an amplitude of 3, a period of 4 π, and a horizontal shift of negative π is $f(x) =3cos(0.5x+\pi )$.

What is a function?

A function is a rule that relates two variables.

The parent function is:

$f(x)=cosx$

We know the period of the parent function is 2π and the amplitude is 1.

For an amplitude of 3, we need to multiply the parent function by 3.

So, the function with amplitude 3 will be given by:

$f(x) =3cosx$

For a period of 4π,  we need to make the argument of the parent function half.

So, $f(x) = 3cos(0.5x)$

A horizontal shift of negative π means, f(x) will become f(x+π)

So, $f(x) =3cos(0.5x+\pi )$.

Therefore, the general equation of a cosine function with an amplitude of 3, a period of 4 π, and a horizontal shift of negative π is $f(x) =3cos(0.5x+\pi )$.

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