Find the amplitude, period, and phase shift of the function. Graph the function. Be sure to label key points. Show at least two periods.
\[
y=6 \cos \left(4 x+\frac{\pi}{2}\right)
\]
What is the amplitude?
6
(Simplify your answer. Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.) What is the period?
\[
\frac{\pi}{2}
\]
(Simplify your answer. Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.) What is the phase shift?
(Simplify your answer. Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.)

Step 1 ：The amplitude of a trigonometric function is the absolute value of the coefficient of the trigonometric part. In this case, the amplitude is \(6\).

Step 2 ：The period of a trigonometric function is the length of one complete cycle. It is given by the formula \(2\pi / |B|\), where B is the coefficient of x in the argument of the trigonometric function. In this case, B is 4, so the period is \(2\pi / 4 = \pi / 2\).

Step 3 ：The phase shift of a trigonometric function is the horizontal shift of the function. It is given by the formula \(-C / B\), where C is the constant in the argument of the trigonometric function. In this case, C is \(\pi / 2\), so the phase shift is \(-\pi / 2 / 4 = -\pi / 8\).

Step 4 ：Final Answer: The amplitude is \(\boxed{6}\), the period is \(\boxed{\frac{\pi}{2}}\), and the phase shift is \(\boxed{-\frac{\pi}{8}}\).