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: 5


$sin~θ=\frac{3}{5}$ $cos~θ=\frac{4}{5}$ $tan~θ=\frac{3}{4}$ $csc~θ=\frac{5}{3}$ $sec~θ=\frac{5}{4}$ $cot~θ=\frac{4}{3}$

Work Step by Step

First, let's evaluate the hypotenuse: $(hyp)^2=(opp)^2+(adj)^2$ $hyp=\sqrt {8^2+6^2}=\sqrt {100}=10$ $sin~θ=\frac{opp}{hyp}=\frac{6}{10}=\frac{3}{5}$ $cos~θ=\frac{adj}{hyp}=\frac{8}{10}=\frac{4}{5}$ $tan~θ=\frac{opp}{adj}=\frac{6}{8}=\frac{3}{4}$ $csc~θ=\frac{hyp}{opp}=\frac{10}{6}=\frac{5}{3}$ $sec~θ=\frac{hyp}{adj}=\frac{10}{8}=\frac{5}{4}$ $cot~θ=\frac{adj}{opp}=\frac{8}{6}=\frac{4}{3}$
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