Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 6 - Section 6.1 - Solving Trigonometric Equations - 6.1 Problem Set - Page 327: 80


$$\frac{1}{2}\left(\sqrt{3}\sin \theta + \cos \theta\right) $$

Work Step by Step

Since $$\sin(x+y)= \sin x\cos y+\cos x\sin y $$ Then \begin{align*} \sin(\theta+30^{\circ})&= \sin \theta\cos 30^{\circ}+\cos \theta\sin 30^{\circ}\\ &= \frac{\sqrt{3}}{2}\sin \theta + \frac{1}{2}\cos \theta\\ &= \frac{1}{2}\left(\sqrt{3}\sin \theta + \cos \theta\right) \end{align*}
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