Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 2 - Review Exercises - Page 94: 21


$3-\displaystyle \frac{2\sqrt{3}}{3}$

Work Step by Step

reference angles: $\left[\begin{array}{lllll} Quadr.: & I & II & III & IV\\ \theta' & \theta & 180^{o}-\theta & \theta-180^{o} & 360^{o}-\theta \end{array}\right]$ $120^{o}$ is in quadrant II, where tangent is negative, reference angle: $180^{o}-120^{o}=60^{o}$ Function Values of Special Angles: $ \tan 120^{o}=-\tan 60^{o}=-\sqrt{3}$ $240^{o}$ is in quadrant III, where cotangent is positive, reference angle: $240^{o}-180^{o}=60^{o}$ Function Values of Special Angles: $\displaystyle \cot 240^{o}=\cot 60^{o}=\frac{\sqrt{3}}{3}$ $\displaystyle \tan^{2}120^{o}-2\cot 240^{o}=(-\sqrt{3})^{2}-2(\frac{\sqrt{3}}{3})$ $=3-\displaystyle \frac{2\sqrt{3}}{3}$
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