Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 5 - Section 5.3 - Trigonometric Graphs - 5.3 Exercises - Page 429: 52

Answer

(a) amplitude $\frac{1}{10}$, period $\pi$, horizontal shift $-\frac{3\pi}{4}$ (b) $y=-\frac{1}{10}cos2(x+\frac{3\pi}{4})$,

Work Step by Step

(a) Based on the standard forms given $y=a\cdot sink(x-b)$ or $y=a\cdot cosk(x-b)$, we can find the amplitude of the function as $|a|=\frac{1}{10}$, the period as $\pi$, and horizontal shift as $b=-\frac{3\pi}{4}$ (b) Since period=$\frac{2\pi}{k}=\pi$, we have $k=2$, and the equation for this case is $y=-\frac{1}{10}cos2(x+\frac{3\pi}{4})$,
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