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: 4

Answer

Fill the blanks with $|a|, \displaystyle \ \ \frac{2\pi}{k}, \ \ b,$ $4, \displaystyle \ \ \frac{2\pi}{3}, \ \ \frac{\pi}{6}.$

Work Step by Step

See: Graphs of Transformations of Sine and Cosine (p. 424) For $y=a\sin k(x-b)$, $(k>0),\qquad$ $y=a\cos k(x-b)$, $(k>0)$ Amplitude: $|a|$, Period: $\displaystyle \frac{2\pi}{k}$, Horizontal shift: $b$ An appropriate interval on which to graph one complete period is $[b, b+(2\pi/k)]$ --------- The first three blanks: $|a|, \displaystyle \ \ \frac{2\pi}{k}, \ \ b.$ For $y=4\displaystyle \sin 3(x-\frac{\pi}{6})$, a=4, k=3, $b=\displaystyle \frac{\pi}{6}.$ Amplitude: $|a|=4$, Period: $\displaystyle \frac{2\pi}{k}=\frac{2\pi}{3}$, Horizontal shift: $b =\displaystyle \frac{\pi}{6}$ Fill the remaining blanks with $4, \displaystyle \ \ \frac{2\pi}{3}, \ \ \frac{\pi}{6}.$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.