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: 48

Answer

a. amplitude=2, period=$\pi$, horizontal shift=0 b. $y=2\cos 2x$

Work Step by Step

For $y=a\sin k(x-b),\ ,\quad y=a\cos k(x-b)$, $(k>0)$ Amplitude: $|a|$, Period: $\displaystyle \frac{2\pi}{k}$, Horizontal shift: $b$ ----------- f(0)$\neq$0, its maximum is at x=0, and after x=0, the graph descends. These are characteristics of a cosine curve with positive a, and no horizontal shift (b=0). The amplitude is 2, a can be $\pm$2, but since it is positive, a=2. The period is $\pi$ (the next unmarked value on the x-axis after $\displaystyle \frac{3\pi}{4}$) So from $\displaystyle \frac{2\pi}{k} =\pi$, it follows that k=2. With these parameters, $f(x)=y=a\cos k(x-b)$ $y=2\cos 2x$ a. amplitude=2, period=$\pi$, horizontal shift=0 b. $y=2\cos 2x$
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