Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 6 - 6.5 - Graphs of Other Trigonometric Functions - 6.5 Exercises - Page 476: 63


The function is even. Notice that the function is symmetric with respect to the y-axis. $f(-x)=f(x)$, that is $(-x)csc(-x)=x~csc~x$

Work Step by Step

$f(x)=x~csc~x$ $f(-x)=(-x)csc(-x)=-x\frac{1}{sin(-x)}=-x\frac{1}{-sin~x}=x\frac{1}{sin~x}=x~csc~x=f(x)$
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