Given the following function:
[tex]\text{ y = 2cos(}\frac{\pi}{2}x)\text{ + 3}[/tex]
We will be using the standard formula aCos (bx - c) + d to find the variables used to find the period.
We get,
aCos (bx - c) + d = 2 cos (π/2x) + 3
a = 2
b = π/2
c = 0
d = 3
Finding the period, we will be using the following formula:
[tex]\text{ Period = }\frac{2\pi}{b}[/tex]
We get,
[tex]\text{ Period = }\frac{2\pi}{b}[/tex][tex]\text{ = }\frac{2\pi}{\frac{\pi}{2}}[/tex][tex]\text{ = 2(}\pi)\text{ x }\frac{2}{(\pi)}[/tex][tex]\text{ = 2 x 2}[/tex][tex]\text{ Period = 4}[/tex]
Therefore, the period of y = 2 cos (π/2x) + 3 is 4. The answer is letter D.
