Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.5 Write Trigonometric Functions and Models - 14.5 Exercises - Skill Practice - Page 944: 3

$y =3 \sin 2x$

General solution for Trigonometric functions $sine$ and $cosine$ that model a sinusoid is as follows: $y=A \sin B (x-h) +k $ and $y=A \cos B (x-h)+k$ We can see from the graph that it passes through the origin and defines the $Sine$ function. Here, the amplitude is $a=3$, that is $3 \sin $ Since, the time period for a trigonometric function is $2 \pi/b$ and here $B=2$ Thus, we have $y =3 \sin 2x$