Final answer:
The cosine function with a midline of y=3, an amplitude of 5, and a period of π is y = 5 cos(2x) + 3. The amplitude and midline directly match the given values, while the period is set by adjusting the coefficient inside the cosine function to 2, as the period is calculated by 2π / B.
Step-by-step explanation:
The student is asking for a cosine function that satisfies certain conditions: a midline at y=3, an amplitude of 5, and a period of π (pi). These conditions help define the necessary parameters for the cosine function.
The general form of a cosine function is y = A cos(Bx + C) + D, where A is the amplitude, B affects the period, C is the phase shift, and D is the midline.
Since the amplitude is 5, A = 5. The midline, which is the vertical shift, is at y=3, so D = 3.
Finally, the period of the function, which is normally 2π for the basic cosine function, is required to be π. The period is calculated by 2π / B, so in our case, B = 2π / π = 2. There is no horizontal phase shift mentioned, so we'll assume C = 0.
The cosine function that meets these requirements is y = 5 cos(2x) + 3, where it has an amplitude of 5, a midline of y=3, and a period of π radians.