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A sinusoidal function whose period is 4π, maximum value is 6, and minimum value is -2 has
a y intercept of 6.
What is the equation of the function described?

Sagot :

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The sinusoidal function described is f(x) = 4*cos(x/2) + 2.

What is the equation of the function described?

First, the amplitude is equal to half of the difference between the maximum and the minimum, so the amplitude is:

A = (6 - (-2))/2 = 4

The midline is equal to the minimum plus the amplitude:

M = -2 + 4 = 2.

now, we know that the y-intercept (when the function is evaluated in x = 0) is 6, so from that we conclude that we have a cosine function:

f(x) = 4*cos(kx) + 2

Notice that when evaluated in zero, we get:

f(0) = 4*cos(0) + 2 = 6.

Finally, we need to find the value of k.

Notice that the period of this function is 4π, while the period of the general cosine function is 2π, then we must have:

k*4π = 2π

Solving for k, we get:

h = (2π)/(4π) = 1/2.

Then the sinusoidal function described is f(x) = 4*cos(x/2) + 2.

If you want to learn more about sinusoidal functions:

https://brainly.com/question/9565966

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