Find the amplitude and period of the function.
\[
y=\cos (4 x)
\]
amplitude
period
Final Answer: The amplitude of the function is \(\boxed{1}\) and the period of the function is \(\boxed{\frac{\pi}{2}}\).
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 \(\boxed{\frac{\pi}{2}}\).