Question

6 multiple choice 1 point what is the equation of the graph? $y=\frac{3}{4}\cos(2x)$ $y=\frac{3}{4}\sin(2x)$ $y=\frac{3}{2}\cos x$ $y=\frac{3}{2}\sin x$

Explanation:

Step1: Determine the amplitude

The general form of a cosine function is \(y = A\cos(Bx)\), where \(A\) is the amplitude. From the graph, the maximum value is \(\frac{3}{4}\) and the minimum is \(-\frac{3}{4}\), so \(A=\frac{3}{4}\).

Step2: Determine the period

The period of \(y = A\cos(Bx)\) is \(T=\frac{2\pi}{B}\). The standard period of \(y = \cos(x)\) is \(2\pi\). From the graph, the period is \(\pi\). Using \(T=\frac{2\pi}{B}\), we substitute \(T = \pi\) and solve for \(B\): \(\pi=\frac{2\pi}{B}\), so \(B = 2\).

Answer:

\(y=\frac{3}{4}\cos(2x)\)