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: 39

Answer

The Amplitude is $ 5$ The Period is $\frac{2\pi}{3}$ The Horizontal shift is $\frac {\pi}{12}$ units to the right See graph below.

Work Step by Step

For $y=a\sin c(x−h) + k$ $y =a \cos c(x−h) + k$, Amplitude: $|a|$, Period: $\frac{2\pi} {|c|}$, Horizontal Shift: h The question asks for a graph, amplitude, period, and horizontal shift of the function. Given $y = 5\sin (3x - \frac{\pi}{4})$ $y = 5\sin 3(x - \frac{\pi}{12})$ The Amplitude is $|5| = 5$ The Period is $\frac{2\pi}{|3|} = \frac{2\pi}{3}$ The Horizontal shift is $\frac {\pi}{12}$ units to the right See graph below.
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