Find the amplitude and period of the function. \[ y=\cos (4 x) \] amplitude period

Step 1 ：Given the function \(y=\cos (4 x)\).

Step 2 ：The amplitude of a cosine function is the absolute value of the coefficient of the cosine term, which in this case is 1.

Step 3 ：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. In this case, \(b=4\), so the period is \(\frac{2\pi}{4} = \frac{\pi}{2}\).

Step 4 ：Final Answer: The amplitude of the function is \(\boxed{1}\) and the period of the function is \(\boxed{\frac{\pi}{2}}\).