Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 13, Trigonometric Ratios and Functions - 13.3 Evaluate Trigonometric Functions of Any Angle - 13.3 Exercises - Skill Practice - Page 871: 30



Work Step by Step

When $P$ is the period of $f(x)$ then we have $ f(x+p)=f(x)$ Here, we have $ \theta= (-\dfrac{3 \pi}{4})$ lies in the third quadrant; thus, we will have to add $2 \pi$ in order to get the co-terminal angle. But $\theta'=\dfrac{-3 \pi}{4}+ 2\pi=\dfrac{5 \pi}{4}$ and $\theta''=\dfrac{5 \pi}{4}-\pi=\dfrac{\pi}{4}$ Thus, we have $\tan(\dfrac{5 \pi}{4})=\tan \dfrac{\pi}{4}$ Hence, $\tan \dfrac{\pi}{4}=1$
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