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: 35


$sin~\frac{\pi}{12}~cos~\frac{\pi}{4}+cos~\frac{\pi}{12}~sin~\frac{\pi}{4}=\frac{\sqrt 3}{2}$

Work Step by Step

$sin(u+v)=sin~u~cos~v+cos~u~sin~v$ $sin~\frac{\pi}{12}~cos~\frac{\pi}{4}+cos~\frac{\pi}{12}~sin~\frac{\pi}{4}=sin(\frac{\pi}{12}+\frac{\pi}{4})=sin(\frac{\pi}{12}+\frac{\pi(3)}{4(3)})=sin(\frac{\pi}{12}+\frac{3\pi}{12})=sin~\frac{4\pi}{12}=sin~\frac{\pi}{3}=\frac{\sqrt 3}{2}$
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