Final answer:
A cosine function with an amplitude of 4, a midline of y = 3, and a period of 5π/3 is represented by the equation y = 4 cos(6/5 x) + 3.
Step-by-step explanation:
To write a cosine function with an amplitude of 4, a midline of y = 3, and a period of 5π/3, we start by considering the standard form of a cosine function, which is y = A cos(B(x - C)) + D, where A is the amplitude, B affects the period, C is the phase shift, and D is the midline. Since we want an amplitude of 4, our A value is 4. The period of a cosine function is 2π/B, so by setting this equal to the given period of 5π/3 we can solve for B, yielding B=2π/(5π/3)=6/5. No phase shift is mentioned, so C is 0. Finally, the midline is the vertical shift, which is 3, so D is 3. Therefore, the complete function is y = 4 cos(6/5 x) + 3.