Answer :

Answer:

[tex]y=0[/tex]

Step-by-step explanation:

We are asked to find the equation of mid-line of the given sinusoidal function.

Since the mid-line of a sinusoidal function is the line that runs between the maximum and minimum y-values of the function. We can consider it the middle y-value.

[tex]\text{Mid-line}=\frac{\text{Maximum value+Minimum value}}{2}[/tex]

We can see from our given graph that the maximum value of our function is 5 and minimum value of our function is -5.

Upon substituting these values in mid-line formula we will get,

[tex]\text{Mid-line}=\frac{5+(-5)}{2}[/tex]

[tex]\text{Mid-line}=\frac{5-5}{2}[/tex]

[tex]\text{Mid-line}=\frac{0}{2}[/tex]

[tex]\text{Mid-line}=0[/tex]

Therefore, the equation of the mid-line of the given sinusoidal function is [tex]y=0[/tex].

The equation of the midline of the sinusoidal function is [tex]\rm y=0[/tex]

Given: Sinusoidal function in the Graph,

As we know that the mid-line of any Sinusoidal function is a line that goes between the higgest and lowest values of y of that function. Here wewill take it the middle value of y.

[tex]\rm Mid- Line = \dfrac{Higgest \;value+ Lowest\; value}{2}[/tex]

Now, here we can see that in given graph the Higgest value of the function is 5 and Lowest value of the function is -5.

On substituting the Higgest value and Lowest value in mid-line formula we get,

[tex]\rm Mid-Line=\dfrac{5+(-5)}{2}\\\\Mid -Line =\dfrac{5-5}{2}\\\\Mid -Line =\dfrac{0}{2}\\[/tex]

Therefore,The equation of the midline of the sinusoidal function is [tex]\rm y=0[/tex].

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