A sine function has a maximum y value of 8 and a minimum y value of -2. The period of the sine function is 4pi, and there is no phase shift/horizontal translation. What is the equation of the sine function?

Step-by-step explanation:

The Sine Function

The general form of the sine function (with no phase shift) is:

Where:

A = Amplitude

ω = angular frequency

M= Midline or vertical shift

The midline can be calculated as the mean value of the maximum and minimum values of the oscillation, thus:

The amplitude is half the difference between the maximum and minimum values of the oscillation:

The angular frequency is calculated in terms of the period T as:

Since T=4π:

Substituting in the general form of the sine function:

The first choice is correct

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step-by-step explanation: