Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 5 - Section 5.6 - Modeling Harmonic Motion - 5.6 Exercises - Page 456: 3

Answer

(a) $|A|$, $\frac{2\pi}{k}$, $b$, $y=A\cdot sin(k(t-\frac{b}{k}))$, $\frac{b}{k}$ (b) $5$, $\frac{\pi}{2}$, $\pi$, $\frac{\pi}{4}$

Work Step by Step

(a) ... the amplitude is $|A|$, the period is $\frac{2\pi}{k}$, and the phase is $b$ ... to get $y=A\cdot sin(k(t-\frac{b}{k}))$ ... the horizontal shift is $\frac{b}{k}$ (b) the amplitude is $5$, the period is $\frac{2\pi}{4}=\frac{\pi}{2}$, the phase is $\pi$, the horizontal shift is $\frac{\pi}{4}$
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