Question

enter the equation for the graph.
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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 of \(y\) is \(3\) and the minimum value is \(- 3\). The formula for amplitude is \(A=\frac{\text{Max}-\text{Min}}{2}\). So, \(A = 3\).

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

The general formula for the period \(T\) of a cosine function \(y = A\cos(Bx)\) is \(T=\frac{2\pi}{B}\). From the graph, the period \(T = 2\pi\). Substituting \(T = 2\pi\) into \(T=\frac{2\pi}{B}\), we get \(2\pi=\frac{2\pi}{B}\), then \(B = 1\).

Answer:

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