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

Explanation:

Step1: Find the amplitude

The amplitude (A) of a cosine function (y = A\cos(Bx)) is the maximum value of (y). From the graph, the maximum value is (1) and the minimum is (- 1). The amplitude (A=\frac{\text{Max}-\text{Min}}{2}=\frac{1 - (-1)}{2}=1)

Step2: Find the period and then (B)

The general formula for the period (T) of (y = A\cos(Bx)) is (T=\frac{2\pi}{B}). From the graph, the period (T=\frac{2\pi}{3}) (from (x = 0) to (x=\frac{2\pi}{3}) is one - full cycle). Using the formula (T=\frac{2\pi}{B}), we substitute (T = \frac{2\pi}{3}) (\frac{2\pi}{3}=\frac{2\pi}{B}), solving for (B) gives (B = 3)

Answer:

(y = 1\cos(3x))