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 - Problem Solving - Page 946: 28a


$d= -6.5 \cos (\dfrac{\pi}{6})t+10$

Work Step by Step

From the table we have $M=16.5 ; m=3.5$ Amplitude, $|a|= \dfrac{M-m}{2}= \dfrac{16.5-3.5}{2}=6.5$ Vertical amplitude, $k= \dfrac{M+m}{2}= \dfrac{16.5+3.5}{2}=10$ Here, the period is: $P=2(6) =12 hours$ and $p=\dfrac{2 \pi}{B}=12 \implies B=\dfrac{\pi}{6}$ We can see that the graph is minimum at $t=0$; this means that we will use the cosine model that is reflected in the x-axis with no horizontal shift, that is, $h=0$ Hence, the model is: $d= -6.5 \cos (\dfrac{\pi}{6})t+10$
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