Question

periodic functions review
(π/2, 5/2)
(2π, 3/2)
(π, 3/2)
(0, 3/2)
(3π/2, 1/2)
-π 0 π 2π 3π x
click for long desc
what is the midline of the sine function?
(1 point)
○ y = 3/2
○ y = 5/2
○ y = 1/2
○ y = 3π/2

Explanation:

Step1: Recall the definition of midline

The midline of a sinusoidal function \(y = A\sin(Bx - C)+D\) is \(y = D\). It is also the horizontal line that is exactly between the maximum and minimum values of the function.

Step2: Find the maximum and minimum values

From the graph, the maximum value \(y_{max}=\frac{5}{2}\) and the minimum value \(y_{min}=\frac{1}{2}\).

Step3: Calculate the midline

The formula for the midline \(y=\frac{y_{max} + y_{min}}{2}\). Substitute \(y_{max}=\frac{5}{2}\) and \(y_{min}=\frac{1}{2}\) into the formula: \(y=\frac{\frac{5}{2}+\frac{1}{2}}{2}=\frac{\frac{5 + 1}{2}}{2}=\frac{3}{2}\) (also, we can observe from the points \((0,\frac{3}{2})\), \((\pi,\frac{3}{2})\), \((2\pi,\frac{3}{2})\) that these points lie on the mid - line of the sinusoidal function)

Answer:

\(y=\frac{3}{2}\)