Final answer:
The equation for the cosine function with the given parameters is f(x) = 3 cos(x + 180) + 5.
Step-by-step explanation:
The cosine function we want to write has a specified amplitude, period, phase shift, and vertical shift. To incorporate these into the function, we use the general form of the cosine function, which is:
f(x) = A cos(B(x - C)) + D,
where:
A is the amplitude,
B is the constant that determines the period,
C is the phase shift, and
D is the vertical shift.
Given that the amplitude is 3, the period is 360 degrees, the phase shift is 180 degrees, and the vertical shift is 5, we can set up our equation as follows:
The amplitude (A) is 3.
The period (P) is 360 degrees, so B = 360/period = 360/360 = 1.
The phase shift (C) is 180 degrees, so we use (+180) in the function.
The vertical shift (D) is 5.
Putting it all together, the equation for the cosine function is:
f(x) = 3 cos(x + 180) + 5.