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: 28b


$t=0,12,24$ for low tide and $t=6, 18$ for high tide

Work Step by Step

From the previous part (a), we have $d= -6.5 \cos (\dfrac{\pi}{6})t+10$ Here, Low Tide $d=3.5$ $3.5= -6.5 \cos (\dfrac{\pi}{6})t+10 \implies \cos (\dfrac{\pi}{6})t=1$ or, $2 \pi n=\dfrac{\pi}{6}t \implies 12n=t$ This gives: $t=0,12,24$ Here, High Tide $d=16.5$ $16.5= -6.5 \cos (\dfrac{\pi}{6})t+10 \implies \cos (\dfrac{\pi}{6})t=-1$ or, $\pi+2 \pi n=\dfrac{\pi}{6}t \implies 6+12n=t$ This gives: $t=6, 18$
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