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: 6


$sin~θ=\frac{5}{13}$ $cos~θ=\frac{12}{13}$ $tan~θ=\frac{5}{12}$ $csc~θ=\frac{13}{5}$ $sec~θ=\frac{13}{12}$ $cot~θ=\frac{12}{5}$

Work Step by Step

First, let's evaluate the side adjacent to $θ$: $(hyp)^2=(opp)^2+(adj)^2$ $13^2=5^2+(adj)^2$ $169-25=(adj)^2$ $144=(adj)^2$ $adj=12$ $sin~θ=\frac{opp}{hyp}=\frac{5}{13}$ $cos~θ=\frac{adj}{hyp}=\frac{12}{13}$ $tan~θ=\frac{opp}{adj}=\frac{5}{12}$ $csc~θ=\frac{hyp}{opp}=\frac{13}{5}$ $sec~θ=\frac{hyp}{adj}=\frac{13}{12}$ $cot~θ=\frac{adj}{opp}=\frac{12}{5}$
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