Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 6 - Review Questions - Page 501: 41


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

Work Step by Step

Distance from the origin to the given point: $d=\sqrt {12^2+16^2}=\sqrt {400}=20$ $sin~\theta=\frac{opp}{hyp}=\frac{16}{20}=\frac{4}{5}$ $cos~\theta=\frac{adj}{hyp}=\frac{12}{20}=\frac{3}{5}$ $tan~\theta=\frac{opp}{adj}=\frac{16}{12}=\frac{4}{3}$ $cot~\theta=\frac{adj}{opp}=\frac{12}{16}=\frac{3}{4}$ $sec~\theta=\frac{hyp}{adj}=\frac{20}{12}=\frac{5}{3}$ $csc~\theta=\frac{hyp}{opp}=\frac{20}{16}=\frac{5}{4}$
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