Graph two full periods of the function $f(x)=\cos (4x)$ and state the amplitude and period.

Enter the exact answers.
For the number $\pi$, either choose $\pi$ from the drop-down menu or type in $\mathrm{Pi}$ (with a capital P).

Amplitude: $A=$
Period: $P=$

Step 1 ：The amplitude of a cosine function is the absolute value of the coefficient of the cosine term. In this case, the coefficient of the cosine term is 1, so the amplitude is $A=1$.

Step 2 ：The period of a cosine function is given by $\frac{2\pi }{|B|}$, where $B$ is the coefficient of $x$ in the argument of the cosine function. In this case, $B$ is 4. So, the period is $\frac{2\pi }{4}=\frac{\pi }{2}$.

Step 3 ：To graph the function, we generate a range of x-values from 0 to 4 times the period (to get two full periods), and then calculate the corresponding y-values using the function $f(x)=\cos (4x)$.

Step 4 ：The graph shows two full periods of the function $f(x)=\cos (4x)$, as expected. The amplitude and period calculated earlier also match with the graph.

Step 5 ：$\boxed{{\displaystyle A=1,P=\frac{\pi }{2}}}$