Question

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?

Answer 1

The equation for the sinusoidal function described is given as follows:

$y = 4\cos{\left(\frac{1}{2}x\right)} + 2$

What is a sinusoidal function?

We want a function with a y-intercept at it's maximum value, hence we use the cosine equation, given by:

$y = A\cos{\left(\frac{2\pi}{B}x\right)} + C$

In which:

• 2A is the amplitude, which is the difference between the largest and smallest value.

• B is the period.

• C is the vertical shift, considering that the standard cosine function has range between -A and A.

The amplitude is of 8, hence 2A = 8 -> A = 4. This would represent a function between -4 and 4, but we want between -2 and 6, hence the vertical shift is of C = 2.

As for the period, we have that:

$B = 4\pi$

Then, the equation is given by:

$y = 4\cos{\left(\frac{1}{2}x\right)} + 2$

More can be learned about sinusoidal functions at https://brainly.com/question/26315885

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