Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 4 - Review Exercises - Page 183: 21

Answer

cotangent

Work Step by Step

Among the six trigonometric functions, only tangent and cotangent have a period of $\pi$. Note that the tangent function is undefined when $x=\frac{\pi}{2}$. Thus, the tangent function cannot be decreasing in the interval $[0, \pi]$. Therefore, the function that satisfies the given descriptions is the cotangent function.
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