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))