Trigonometry 7th Edition

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

Chapter 4 - Section 4.1 - Basic Graphs - 4.1 Problem Set - Page 192: 43

Answer

$-\frac{\sqrt 2}{2}$

Work Step by Step

Since sine is an odd function, $\sin(-\frac{3\pi}{4})=-\sin(\frac{3\pi}{4})$ Using the unit circle, $\frac{3\pi}{4}$ falls in the second quadrant, where sine is positive. By using the identity $\sin(\pi-\theta)=\sin(\theta)$, $-\sin(\frac{3\pi}{4})=-\sin(\pi-\frac{\pi}{4})=-\sin(\frac{\pi}{4})$ $\frac{\pi}{4}$ is a special angle, $-\sin(\frac{\pi}{4})=-\frac{\sqrt 2}{2}$ Therefore, $\sin(-\frac{3\pi}{4})=-\frac{\sqrt 2}{2}$
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