Graph the following function over a two-period interval. Give the period and the amplitude.
\[
y=\frac{1}{5} \cos \frac{\pi}{2} x
\]
What is the period of the function $y=\frac{1}{5} \cos \frac{\pi}{2} x$ ?
(Simplify your answer. Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.)
What is the amplitude of the function $y=\frac{1}{5} \cos \frac{\pi}{2} x$ ?
(Type an integer or a simplified fraction.)
Graph the function $y=\frac{1}{5} \cos \frac{\pi}{2} x$. Choose the correct graph below.
A.
B.
c.
D.

Step 1 ：The graph of $y=\frac{1}{5} \cos \frac{\pi}{2} x$ passes through one full period as $\frac{\pi}{2} x$ ranges from $0$ to $2\pi,$ which means $x$ ranges from $0$ to $\boxed{4}.$

Step 2 ：The amplitude of the function $y=\frac{1}{5} \cos \frac{\pi}{2} x$ is the absolute value of the coefficient of the cosine function, which is $\boxed{\frac{1}{5}}$.

Step 3 ：To graph the function $y=\frac{1}{5} \cos \frac{\pi}{2} x$, we note that the function has a period of $4$ and an amplitude of $\frac{1}{5}$. The function starts at its maximum value of $\frac{1}{5}$ at $x=0$, decreases to $0$ at $x=1$, reaches its minimum value of $-\frac{1}{5}$ at $x=2$, returns to $0$ at $x=3$, and finally returns to its maximum value at $x=4$. This pattern repeats every $4$ units.