Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 7 - Trigonometry and Periodic Functions - Review Exercises and Problems for Chapter Seven - Page 316: 42

Answer

midline: $y=7$ period = $2$ amplitude = $2$

Work Step by Step

Rewrite the equation by dividing by $6$ to get $$y=\frac{12}{6}\sin(\pi t -7)+\frac{42}{6}$$ $$y=2\sin(\pi t -7)+7$$ Equate this equation to the formula $$y=A\cos(B(t-h))+k$$ where $|A|$ is the amplitude, $2\pi/|B|$ is the period, and the midline is $y=k$. Using this form for the equation gives amplitude equal to $|2|=2$, period equal to $2\pi/\pi=2$, and midline $y=7$.
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