Final answer:
To write a sine function with a midline of y = 5, an amplitude of 4, and a period of 4π/3, the function is y = 4 sin((3/2)x) + 5.
Step-by-step explanation:
To write a sine function with a midline of y = 5, an amplitude of 4, and a period of 4π/3, we can start with the general form of a sine function: y = A sin(Bx - C) + D, where A is the amplitude, B determines the period, C is the phase shift, and D is the vertical shift.
Given that the midline is y = 5, we know the vertical shift is D = 5.
Since the amplitude is 4, we have A = 4.
The period is given as 4π/3, which means B = 2π/(4π/3) = 3/2.
Finally, since there is no phase shift, C = 0.
Putting it all together, the sine function that satisfies the given conditions is: y = 4 sin((3/2)x) + 5.