Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix D - Trigonometry - D Exercises - Page A32: 30


$sin \alpha=\frac{2\sqrt 5}{5}$ $cos \alpha=\frac{\sqrt 5}{5}$ $csc \alpha=\frac{\sqrt 5}{2}$ $sec \alpha=\sqrt 5$ $cot \alpha=\frac{1}{2}$

Work Step by Step

Since $tan \alpha=2$, we can label the opposite side as having length 2 and the adjacent side as having length 1. Then Pythagorean Theorem gives hypotenuse side $=\sqrt {2^{2}+1^{2}}=\sqrt 5$ The other five trigonometric functions are given as follows: $sin \alpha=\frac{2\sqrt 5}{5}$ $cos \alpha=\frac{\sqrt 5}{5}$ $csc \alpha=\frac{\sqrt 5}{2}$ $sec \alpha=\sqrt 5$ $cot \alpha=\frac{1}{2}$
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