Algebra and Trigonometry 10th Edition

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

Chapter 7 - 7.4 - Sum and Difference Formulas - 7.4 Exercises - Page 538: 8


(a) $\frac{1}{2}$ (b) $-\frac{1+\sqrt 3}{2}$

Work Step by Step

$sin(u-v)=sin~u~cos~v-cos~u~sin~v$ (a) $sin(\frac{7\pi}{6}-\frac{\pi}{3})=sin~\frac{7\pi}{6}~cos~\frac{\pi}{3}-cos~\frac{7\pi}{6}~sin~\frac{\pi}{3}=-\frac{1}{2}~\frac{1}{2}-(-\frac{\sqrt 3}{2})\frac{\sqrt 3}{2}=-\frac{1}{4}+\frac{3}{4}=\frac{2}{4}=\frac{1}{2}$ (b) $sin~\frac{7\pi}{6}-sin~\frac{\pi}{3}=-\frac{1}{2}-\frac{\sqrt 3}{2}=-\frac{1+\sqrt 3}{2}$
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