Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 4 - Test - Page 187: 4e

Answer

$\frac{\pi}{4}$ units to the left

Work Step by Step

We first write the equation in the form $y=c+a \cos [b(x-d)]$. Therefore, $y=3-6\sin (2x+\frac{\pi}{2})$ becomes $y=3-6\sin [2(x+\frac{\pi}{4})]$. Comparing the equation to its general form, we find that $d=-\frac{\pi}{4}$. $d$ is the phase shift and the phase shift is $d$ units to the right if $d\gt0$. If $d\lt0$, the phase shift is $|d|$ units to the left. Since $d$ is less than zero, the phase shift is $|d|=|-\frac{\pi}{4}|=\frac{\pi}{4}$ units to the left.
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