Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.5 Write Trigonometric Functions and Models - 14.5 Exercises - Skill Practice - Page 944: 5


$y =-2 \cos (\dfrac{\pi}{2}) x +4$

Work Step by Step

General solution for Trigonometric functions $sine$ and $cosine$ that model a sinusoid is as follows: $y=A \sin B (x-h) +k $ and $y=A \cos B (x-h)+k$ Here, the amplitude is $A=2$ and we can see from the graph that it has flipped nature which means that we have $-2 \cos $ function. Since the time period for a trigonometric function is $4$ and here $B=\dfrac{\pi}{2}$, the midline of the graph has been shifted by $4$ vertically. Thus, we have $y =-2 \cos (\dfrac{\pi}{2}) x +4$
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