Graph the following function over a two-period interval. Give the period and the amplitude.
\[
y=\frac{1}{4} \cos \frac{\pi}{4} x
\]
What is the period of the function $y=\frac{1}{4} \cos \frac{\pi}{4} x$ ?
(Type an exact answer, using $\pi$. Use fractions for any numbers in the expression.)
Answer
Final Answer: The period of the function \(y=\frac{1}{4} \cos \frac{\pi}{4} x\) is \(\boxed{8}\)
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 \(\boxed{8}\)
