Answer:
y = 0
Step-by-step explanation:
The given sinusoidal equation is [tex]y = 2 \cdot sin \left(\dfrac{\pi}{2} \cdot x + 3 \right)[/tex]
The general form of the sin function is presented as follows;
y = A·sin(B·(x - C)) + D
Where;
A = The amplitude
The period, T = 2·π/B
The frequency, f = B/2·π
C = The horizontal shift
D = The vertical shift
By comparison with the given sine function, we have;
The amplitude, A = 2
The frequency, f = B/2·π = π/2/(2·π) = 1/4
The frequency, f = 1/4 Hz
C = The horizontal shift = 3/(π/2) = 6/π
The vertical shift, D = 0
Given that the mid line of the parent function, sin(x), is the line y = 0, and that the vertical shift is 0, the midline of the function, [tex]y = 2 \cdot sin \left(\dfrac{\pi}{2} \cdot x + 3 \right)[/tex], is therefore, the line;
y = 0.
