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: 63

Answer

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

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 $[\pi,\displaystyle \frac{3\pi}{2}]$, (quadrant III), we search for a point (x,y) on the unit circle, such that $\displaystyle \frac{y}{x}=\sqrt{3}$ We find the point$:$ $(-\displaystyle \frac{\sqrt{3}}{2},-\frac{1}{2}) $ assigned to $240^{o}$, or $\displaystyle \frac{4\pi}{3}$ rad. $\displaystyle \tan\frac{4\pi}{3}=\frac{-\frac{\sqrt{3}}{2}}{-\frac{1}{2}}=\sqrt{3},$ $s = \displaystyle \frac{4\pi}{3}$
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