Final answer:
The cosine function with a period of π/3, amplitude of 2, and midline of y = -4 is y(x) = 2*cos(6x) - 4.
Step-by-step explanation:
To write a cosine function with a period of π/3, an amplitude of 2, and a midline of y = -4, recall that the general form of a cosine function is A*cos(Bx - C) + D, where A is the amplitude, the period is 2π/B, C is the phase shift, and D is the midline. Since we want the period to be π/3, we find B by setting 2π/B = π/3, giving us B = 6. The function will have no horizontal phase shift (C = 0) as it is not specified, resulting in the wave function:
y(x) = 2*cos(6x) - 4
This function oscillates between +2 and -2 about the midline y = -4 with a period of π/3.