Trigonometry (11th Edition) Clone

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

Chapter 3 - Radian Measure and the Unit Circle - Section 3.1 Radian Measure - 3.1 Exercises - Page 105: 86



Work Step by Step

Convert the angle measure to degrees to obtain: $=-\frac{13\pi}{3} \cdot \frac{180^o}{\pi} = -13(60)^o=-780^o$ Thus, $\csc{(-\frac{13\pi}{3})} = \csc{(-780^o)}$ $-780^o$ is co-terminal with $-780^o+1080^o=300^o$. $300^o$ is in Quadrant IV so its reference angle is $=360^o-300^o=60^o$. Note that the cosecant function is positive in Quadrant IV. From Section 2.1 (page 50) , we learned that: $\csc{60^o} = \dfrac{2\sqrt3}{3}$ This means that: $\csc{(-\frac{13\pi}{3})} \\=\csc{(-780^o)} \\=\csc{60^o} \\= \dfrac{2\sqrt3}{3}$
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