enter the equation for the graph.\ny = ? cos( x)

Explanation:

Step1: Determine the amplitude

The amplitude $A$ of a cosine - function $y = A\cos(Bx)$ is half the distance between the maximum and minimum values of the function. The maximum value of the given graph is $y = 1$ and the minimum value is $y=-1$. So, $A=\frac{1 - (- 1)}{2}=1$.

Step2: Determine the period and find $B$

The period $T$ of a cosine - function $y = A\cos(Bx)$ is given by the formula $T=\frac{2\pi}{B}$. From the graph, we can see that the period $T=\frac{2\pi}{3}$. Using the formula $T = \frac{2\pi}{B}$, we substitute $T=\frac{2\pi}{3}$ and solve for $B$: $\frac{2\pi}{3}=\frac{2\pi}{B}$, which gives $B = 3$.

Answer:

$y = 1\cos(3x)$