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: 10


$y= 4 \cos x$

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 $y=A \cos B (x-h)+k$ Amplitude, $|a|= \dfrac{M-m}{2}= \dfrac{4-(-4)}{2}= \dfrac{8}{2}$ Thus, we have $|a|=4$ Vertical amplitude, $k= \dfrac{M+m}{2}= \dfrac{4-4}{2}$ This gives: $|k|=0$ Therefore, the period is: $P=2( \pi-0) =2 \pi$ and $\dfrac{2 \pi}{a}=2 \pi \implies a=1$ Hence, the function is: $y= 4 \cos x$
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