Write a cosine function that has a midline of y, equals, 5, commay=5, an amplitude of 2 and a period of start fraction, pi, divided by, 2, end fraction 2π​ .

The general form of a cosine function is y = A cos(B(x - C)) + D, where:

• A is the amplitude
• B is the frequency, which is related to the period by the formula B = 2π / period
• C is the phase shift, which is the horizontal shift
• D is the midline, which is the vertical shift

Given that the midline is y = 5, the amplitude is 2, and the period is π/2, we can substitute these values into the general form to get the specific cosine function.

First, calculate B using the given period: B = 2π / (π/2) = 4.

Since no phase shift is mentioned, we can assume C = 0.

Substituting A = 2, B = 4, C = 0, and D = 5 into the general form gives:

y = 2 cos(4x) + 5

So, the cosine function that meets the given conditions is y = 2 cos(4x) + 5.