find the amplitude and period of the function. y = cos(8πx) amplitude period

Explanation:

Step1: Recall amplitude formula

For $y = A\cos(Bx)$, amplitude is $|A|$. Here $A = 1$, so amplitude $=|1| = 1$.

Step2: Recall period formula

For $y=\cos(Bx)$, period is $\frac{2\pi}{|B|}$. Here $B = 8\pi$, so period $=\frac{2\pi}{|8\pi|}=\frac{2\pi}{8\pi}=\frac{1}{4}$.

Answer:

amplitude: 1 period: $\frac{1}{4}$