Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 3 - Radian Measure and the Unit Circle - Section 3.3 The Unit Circle and Circular Functions - 3.3 Exercises - Page 118: 67

Answer

$s = \displaystyle \frac{4\pi}{3}$ or $\displaystyle \frac{5\pi}{3}$

Work Step by Step

For any real number $s$ represented by a directed arc on the unit circle, $\sin s=y\quad \cos s=x \quad \displaystyle \tan s=\frac{y}{x} (x\neq 0)$ Use Figure 13 on page 111. ---------------- In the interval $[0,2\pi)$, (the unit circle), we search for points (x,y), such that $y=-\displaystyle \frac{\sqrt{3}}{2}$ $(\sin s=y)$ We find points$:$ $(-\displaystyle \frac{1}{2},-\displaystyle \frac{\sqrt{3}}{2}) \quad $in quadrant III, assigned to $240^{o}$, or $\displaystyle \frac{4\pi}{3}$ rad. and $(\displaystyle \frac{1}{2},-\displaystyle \frac{\sqrt{3}}{2})\quad $in quadrant IV, assigned to $300^{o}$, or $\displaystyle \frac{5\pi}{3}$ rad. $s = \displaystyle \frac{4\pi}{3}$ or $\displaystyle \frac{5\pi}{3}$
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