Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

APPENDIX D - Trigonometry - D Exercises: 23

Answer

$sin\frac{3\pi}{4}=sin\frac{\pi}{4}=\frac{\sqrt 2}{2}$ $csc\frac{3\pi}{4}=\frac{1}{sin\frac{3\pi}{4}}=\sqrt 2$ $cos\frac{3\pi}{4}=-cos\frac{\pi}{4}=-\frac{\sqrt 2}{2}$ $sec\frac{3\pi}{4}=\frac{1}{cos\frac{3\pi}{4}}=-\sqrt 2$ $tan\frac{3\pi}{4}=-tan\frac{\pi}{4}=-1$ $cot\frac{3\pi}{4}=\frac{1}{tan\frac{3\pi}{4}}=-1$

Work Step by Step

Since $\frac{3\pi}{4}$ lies in the second quadrant, its reference angle will be $\pi-\frac{3\pi}{4}=\frac{\pi}{4}$, which can be considered as a common angle to all trigonometric ratios. The trigonometric ratios and their inverse trigonometric ratios are given as follows: $sin\frac{3\pi}{4}=sin\frac{\pi}{4}=\frac{\sqrt 2}{2}$ $csc\frac{3\pi}{4}=\frac{1}{sin\frac{3\pi}{4}}=\sqrt 2$ $cos\frac{3\pi}{4}=-cos\frac{\pi}{4}=-\frac{\sqrt 2}{2}$ $sec\frac{3\pi}{4}=\frac{1}{cos\frac{3\pi}{4}}=-\sqrt 2$ $tan\frac{3\pi}{4}=-tan\frac{\pi}{4}=-1$ $cot\frac{3\pi}{4}=\frac{1}{tan\frac{3\pi}{4}}=-1$
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