Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 13 - The Trigonometric Functions - 13.1 Definitions of the Trigonometric Functions - 13.1 Exercises - Page 678: 47


$\sin \frac{-7\pi}{6}=\frac{-1}{2}$

Work Step by Step

We are given $\sin \frac{-7\pi}{6}$ $\sin(\frac{-7\pi}{6}+\pi)=\sin(\frac{-\pi}{6})$ convert $\frac{\pi}{6}$ radians to degrees $\frac{\pi}{6}=\frac{\pi}{6}(\frac{180^\circ}{\pi})$ $\frac{\pi}{6}=30^\circ$ $\sin \frac{-7\pi}{6}=-(\sin 30^\circ)$ $\sin30^\circ=\frac{1}{2}$ so $\sin \frac{-7\pi}{6}=\frac{-1}{2}$
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