Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.5 Write Trigonometric Functions and Models - 14.5 Exercises - Skill Practice - Page 944: 4

$y =5 \cos 4x$

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 $cosine$ function. Here, the amplitude is $A=5$, that is $5 \cos $. Since, the time period for a trigonometric function is $4 \pi/B$ and here $B=4$, we find: Thus, we have $y =5 \cos 4x$