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: 7


$sin~θ=\frac{9}{41}$ $cos~θ=\frac{40}{41}$ $tan~θ=\frac{9}{40}$ $csc~θ=\frac{41}{9}$ $sec~θ=\frac{41}{40}$ $cot~θ=\frac{40}{9}$

Work Step by Step

First, let's evaluate the side adjacent to $θ$: $(hyp)^2=(opp)^2+(adj)^2$ $41^2=9^2+(adj)^2$ $1681-81=(adj)^2$ $1600=(adj)^2$ $adj=40$ $sin~θ=\frac{opp}{hyp}=\frac{9}{41}$ $cos~θ=\frac{adj}{hyp}=\frac{40}{41}$ $tan~θ=\frac{opp}{adj}=\frac{9}{40}$ $csc~θ=\frac{hyp}{opp}=\frac{41}{9}$ $sec~θ=\frac{hyp}{adj}=\frac{41}{40}$ $cot~θ=\frac{adj}{opp}=\frac{40}{9}$
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