Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 1 - Section 1.4 - Introduction to Identities - 1.4 Problem Set - Page 40: 19

Answer

$\tan\theta$ = 2

Work Step by Step

Ratio identity for $\tan\theta$ is- $\tan\theta$ = $\frac{\sin\theta}{\cos\theta}$ Substituting given values of $\sin\theta$ and $\cos\theta$- $\tan\theta$ = $\frac{\frac{2\sqrt 5}{5}}{\frac{\sqrt 5}{5}}$ = $\frac{2\sqrt 5 \times 5}{5\sqrt 5}$ = 2 or $\tan\theta$ = 2
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