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: 64


The function is odd. Notice that the function is symmetric with respect to the origin. $f(-x)=-f(x)$, that is $(-x)^2cot(-x)=-x^2cot~x$

Work Step by Step

$f(x)=x^2cot~x$ $f(-x)=(-x)^2cot(-x)=x^2\frac{cos(-x)}{sin(-x)}=x^2\frac{cos~x}{-sin~x}=-x^2\frac{cos~x}{sin~x}=-x^2cot~x=-f(x)$
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