Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - 1.4 Trigonometric Functions - Exercises - Page 31: 57


Both $\tan θ$ and $\cot θ$ are periodic with period $\pi$.

Work Step by Step

Since \begin{aligned} &\tan (\theta+\pi)=\frac{\sin (\theta+\pi)}{\cos (\theta+\pi)}=\frac{-\sin \theta}{-\cos \theta}=\tan \theta\\ &\cot (\theta+\pi)=\frac{\cos (\theta+\pi)}{\sin (\theta+\pi)}=\frac{-\cos \theta}{-\sin \theta}=\cot \theta \end{aligned} Then both $\tan θ$ and $\cot θ$ are periodic with period $\pi$.
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