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: 13


$y= 7+2 \cos (\dfrac{4}{5}) (x-\dfrac{ 3\pi}{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 $y=A \cos B (x-h)+k$ Amplitude, $|a|= \dfrac{M-m}{2}= \dfrac{9-5}{2}= \dfrac{4}{2}$ Thus, we have $|a|=2$ Vertical amplitude, $k= \dfrac{M+m}{2}= \dfrac{9+5}{2}$ This gives: $|k|=7$ Therefore, the period is: $P=2(2 \pi- \dfrac{ 3\pi}{4}) =\dfrac{5\pi}{2}$ and $\dfrac{2 \pi}{a}=\dfrac{ 5\pi}{2} \implies a=\dfrac{4}{5}$ Here, the phase difference is: $\dfrac{ 3\pi}{4}$ Hence, the function is: $y= 7+2 \cos (\dfrac{4}{5}) (x-\dfrac{ 3\pi}{4}) $
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