Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix D - Trigonometry - D Exercises - Page A32: 25


$sin\frac{9\pi}{2}=1$ $cos\frac{9\pi}{2}=0$ $tan\frac{9\pi}{2}= undefined$ $csc\frac{9\pi}{2}=1$ $sec\frac{9\pi}{2}=undefined$ $cot\frac{9\pi}{2}=0$

Work Step by Step

Since, $\frac{9\pi}{2}$ is coterminal angle with $\frac{\pi}{2}$ i.e at positive y-axis, which can be considered as common angle to all trigonometric ratios. The trigonometric ratios and their inverse trigonometric ratios are given as follows: $sin\frac{9\pi}{2}=sin\frac{\pi}{2}=1$ $cos\frac{9\pi}{2}=cos\frac{\pi}{2}=0$ $tan\frac{9\pi}{2}=tan\frac{\pi}{2} = undefined$ $csc\frac{9\pi}{2}=\frac{1}{sin\frac{9\pi}{2}}=1$ $sec\frac{9\pi}{2}=\frac{1}{cos\frac{9\pi}{2}}=undefined$ $cot\frac{9\pi}{2}=\frac{1}{tan\frac{9\pi}{2}}=0$
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