Question

Please help asap! thx

Answer 1

y = 0

Explanation:

The given sinusoidal equation is
`y = 2 \cdot sin \left((\pi)/(2) \cdot x + 3 \right)`

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,
`y = 2 \cdot sin \left((\pi)/(2) \cdot x + 3 \right)`, is therefore, the line;

y = 0.