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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?

A sine function has a maximum y value of 8 and a minimum y value of -2. The period-example-1
User Gtzinos
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1 Answer

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Answer:


\displaystyle y = 5\sin((1)/(2) x) +3

Explanation:

The Sine Function

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


y = A\sin(\omega x) +M

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:


M=(8-2)/(2)=3

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


A=(8+2)/(2)=5

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


\displaystyle \omega=(2\pi)/(T)

Since T=4π:


\displaystyle \omega=(2\pi)/(4 \pi)=(1)/(2)

Substituting in the general form of the sine function:


\boxed{\displaystyle y = 5\sin((1)/(2) x) +3}

The first choice is correct

User Fissure King
by
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