Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 6 - 6.4 - Graphs of Sine and Cosine Functions - 6.4 Exercises - Page 464: 16

Answer

The amplitude and period are the same but for shift, $g$ is shifted $\frac{\pi}{3}$ to the right from $f$.

Work Step by Step

The standard form to use is: $$y=a\sin b(x-c)$$ For function $f(x)=\sin 3x=1\sin 3(x-0)$: $a=1$ $period=\frac{2\pi}{b}=\frac{2\pi}{3}$ $shift=none$ For function $g(x)=\sin (-3x)=\sin (3x-\pi)=1\sin 3\left(x-\frac{\pi}{3}\right)$: $a=1$ $period=\frac{2\pi}{b}=\frac{2\pi}{3}$ $shift=\frac{\pi}{3}~to~the ~right$ Thus, the amplitude and period are the same but for shift, $g$ is shifted $\frac{\pi}{3}$ to the right from $f$.
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