Question

type the equation for the graph below. $y = ?\sin( x)$

Explanation:

Step1: Find the amplitude

The amplitude \(A\) of a sine function \(y = A\sin(Bx)\) is the maximum value from the mid - line. The mid - line is \(y = 0\), and the maximum value \(y = 1\). So, \(A=1\).

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

The general formula for the period \(T\) of a sine function \(y=\sin(Bx)\) 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: \(\frac{2\pi}{3}=\frac{2\pi}{B}\).
Cross - multiply: \(2\pi B=6\pi\).
Divide both sides by \(2\pi\): \(B = 3\).

Answer:

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