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 441: 17


$sin~\theta=\frac{opp}{hyp}=\frac{\sqrt {11}}{6}$ $cos~\theta=\frac{adj}{hyp}=\frac{5}{6}$ $tan~\theta=\frac{opp}{adj}=\frac{\sqrt {11}}{5}$ $cot~\theta=\frac{adj}{opp}=\frac{5\sqrt {11}}{11}$ $csc~\theta=\frac{hyp}{opp}=\frac{6\sqrt {11}}{11}$

Work Step by Step

$sec~\theta=\frac{hyp}{adj}$ $\frac{6}{5}=\frac{hyp}{adj}$ Use the pythagorean theorem to find the opposite side of $\theta$ $6^2=5^2+opp^2$ $opp^2=36-25=11$ $opp=\sqrt {11}$ $sin~\theta=\frac{opp}{hyp}=\frac{\sqrt {11}}{6}$ $cos~\theta=\frac{adj}{hyp}=\frac{5}{6}$ $tan~\theta=\frac{opp}{adj}=\frac{\sqrt {11}}{5}$ $cot~\theta=\frac{adj}{opp}=\frac{5}{\sqrt {11}}=\frac{5\sqrt {11}}{11}$ $csc~\theta=\frac{hyp}{opp}=\frac{6}{\sqrt {11}}=\frac{6\sqrt {11}}{11}$
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