Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix D - Trigonometry - D Exercises: 29

Answer

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

Work Step by Step

Since $sin \theta=\frac{3}{5}$, we can label the opposite side as having length 3 and the hypotenuse as having length 5. Then Pythagorean Theorem gives adjacent side $=\sqrt {5^{2}-3^{2}}=4$ The other five trigonometric functions are given as follows: $cos \theta=\frac{4}{5}$ $tan \theta=\frac{3}{4}$ $csc \theta=\frac{5}{3}$ $sec \theta=\frac{5}{4}$ $cot \theta=\frac{4}{3}$
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