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: 22


(a) $sin~2u=-\frac{24}{25}$ (b) $cos~2u=\frac{7}{25}$ (c) $tan~2u=-\frac{24}{7}$

Work Step by Step

$cos^2u+sin^2u=1$ $(-\frac{4}{5})^2+sin^2u=1$ $sin^2u=1-\frac{16}{25}=\frac{9}{25}$ $sin~u=+\frac{3}{5}~~~~$ ($\frac{\pi}{2}\lt u\lt\pi$) $tan~u=\frac{sin~u}{cos~u}=\frac{\frac{3}{5}}{-\frac{4}{5}}=-\frac{3}{4}$ (a) $sin~2u=2~sin~u~cos~u=2(\frac{3}{5})(-\frac{4}{5})=-\frac{24}{25}$ (b) $cos~2u=cos^2u-sin^2u=\frac{16}{25}-\frac{9}{25}=\frac{7}{25}$ (c) $tan~2u=\frac{2~tan~u}{1-tan^2u}=\frac{2(-\frac{3}{4})}{1-(-\frac{3}{4})^2}=\frac{-\frac{3}{2}}{\frac{7}{16}}=-\frac{24}{7}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.