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: 21


$sin~\theta=\frac{opp}{hyp}=\frac{\sqrt {10}}{10}$ $cos~\theta=\frac{adj}{hyp}=\frac{3\sqrt {10}}{10}$ $tan~\theta=\frac{opp}{adj}=\frac{1}{3}$ $csc~\theta=\frac{hyp}{opp}=\sqrt {10}$ $sec~\theta=\frac{hyp}{adj}=\frac{\sqrt {10}}{3}$

Work Step by Step

$cot~\theta=\frac{adj}{opp}$ $3=\frac{adj}{opp}$ Use the pythagorean theorem to find the hypotenuse. $hyp^2=1^2+3^2$ $hyp^2=1+9=10$ $hyp=\sqrt {10}$ $sin~\theta=\frac{opp}{hyp}=\frac{1}{\sqrt {10}}=\frac{\sqrt {10}}{10}$ $cos~\theta=\frac{adj}{hyp}=\frac{3}{\sqrt {10}}=\frac{3\sqrt {10}}{10}$ $tan~\theta=\frac{opp}{adj}=\frac{1}{3}$ $csc~\theta=\frac{hyp}{opp}=\frac{\sqrt {10}}{1}=\sqrt {10}$ $sec~\theta=\frac{hyp}{adj}=\frac{\sqrt {10}}{3}$
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