Step 1 :Given the function \(y=\frac{1}{4} \cos \frac{\pi}{4} x\)
Step 2 :The period of a cosine function is given by the formula \(2\pi / B\), where \(B\) is the coefficient of \(x\) in the function.
Step 3 :In this case, \(B = \frac{\pi}{4}\)
Step 4 :So the period of the function is \(2\pi / \frac{\pi}{4} = 8\)
Step 5 :Final Answer: The period of the function \(y=\frac{1}{4} \cos \frac{\pi}{4} x\) is \(\boxed{8}\)