Algebra and Trigonometry 10th Edition

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

Chapter 7 - 7.5 - Multiple-Angle and Product-to-Sum Formulas - 7.5 Exercises - Page 548: 23


(a) $sin~2u=\frac{15}{17}$ (b) $cos~2u=\frac{8}{17}$ (c) $tan~2u=\frac{15}{8}$

Work Step by Step

$sec^2u=tan^2u+1$ $sec^2u=(\frac{3}{5})^2+1=\frac{34}{25}$ $sec~u=\frac{\sqrt {34}}{5}~~~~$ ($0\lt u\lt\frac{\pi}{2}$) $cos~u=\frac{1}{sec~u}=\frac{5}{\sqrt {34}}=\frac{5\sqrt {34}}{34}$ $tan~u=\frac{sin~u}{cos~u}$ $\frac{3}{5}=\frac{sin~u}{\frac{5\sqrt {34}}{34}}$ $sin~u=\frac{3}{5}\frac{5\sqrt {34}}{34}=\frac{3\sqrt {34}}{34}$ (a) $sin~2u=2~sin~u~cos~u=2(\frac{3\sqrt {34}}{34})(\frac{5\sqrt {34}}{34})=\frac{15}{17}$ (b) $cos~2u=cos^2u-sin^2u=\frac{25}{34}-\frac{9}{34}=\frac{8}{17}$ (c) $tan~2u=\frac{2~tan~u}{1-tan^2u}=\frac{2(\frac{3}{5})}{1-(\frac{3}{5})^2}=\frac{\frac{6}{5}}{\frac{16}{25}}=\frac{15}{8}$
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