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

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

Step 5 ：\(\boxed{A=1, P=\frac{\pi}{2}}\)