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

Cosine function have general form for which amplitude, period and phase shift can be specified. The needed equation is y = 3cos(x/2 + π/2)

Suppose that the cosine function has:

Then, its equation is given as:

y = a.cos(bx +c)

For the given context, we have:

Amplitude = a = 3

Period= 4pi

and Horizontal shift = π(since -pi is left and we need only magnitude of shift to left)

Since period = , thus, getting value of b:

= 4π, b = 1/2

And now, as horizontal shift = c/b = π, thus, c = bπ = π/2

Thus, the cosine function needed is given as:

y = a.cos(bx+c) = 3cos(x/2 + π/2)

Its graph is plotted below, with the standard graph of y = cos(x) for comparison.

Thus,

The needed equation is y = 3cos(x/2 + π/2)

Learn more about general cosine function here:

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step-by-step explanation:

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