Write a sine function that has a midline of y, equals, 3, commay=3, an amplitude of 2 and a period of 4, pi4π.
The sine function can be written as:
y = A * sin(B(x - C)) + D
where:
A = amplitude
B = 2π / period
C = horizontal shift
D = midline
For the given parameters:
Amplitude (A) = 2
Period (P) = 4π
Midline (D) = 3
Let's calculate B:
B = 2π / P
B = 2π / (4π)
B = 1/2
Now, since the midline is at y = 3, we set D = 3.
Therefore, the sine function is:
y = 2 * sin((1/2)x) + 3