Question

enter the equation for the graph.

submit

Explanation:

Step1: Determine the amplitude

The amplitude \( A \) of a cosine function \( y = A\cos(Bx) \) is the maximum distance from the mid - line. The mid - line of the given graph is \( y = 0 \). The maximum value is \( y = 1 \) and the minimum value is \( y=-1 \). So, \( A = 1 \).

Step2: Determine the period and then \( B \)

The general formula for the period \( T \) of a cosine function \( y=\cos(Bx) \) is \( T=\frac{2\pi}{B} \).
From the graph, the period \( T=\frac{2\pi}{3} \).
Using the formula \( T = \frac{2\pi}{B} \), we substitute \( T=\frac{2\pi}{3} \) into it:

$$
LATEXBLOCK0
$$

Answer:

\( y = 1\cos(3x) \)