Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 6 - 6.2 - Right Triangle Trigonometry - 6.2 Exercises - Page 442: 38

Answer

(a) $cos~\theta=\frac{1}{5}$ (b) $cot~\theta=\frac{\sqrt 6}{12}$ (c) $cot(90°-\theta)=2\sqrt 6$ (d) $sin~\theta=\frac{2\sqrt 6}{5}$

Work Step by Step

(a) $cos~\theta=\frac{1}{sec~\theta}=\frac{1}{5}$ (b) $1+tan^2\theta=sec^2\theta$ $tan^2\theta=5^2-1=24$ $tan~\theta=2\sqrt 6$ $cot~\theta=\frac{1}{tan~\theta}=\frac{1}{2\sqrt 6}=\frac{\sqrt 6}{12}$ (c) $cot(90°-\theta)=tan~\theta=2\sqrt 6$ (d) $sin^2~\theta+cos^2\theta=1$ $sin^2\theta=1-(\frac{1}{5})^2=\frac{24}{25}$ $sin~\theta=\frac{2\sqrt 6}{5}$
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