Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 7 - Analytic Trigonometry - 7.6 Double-angle and Half-angle Formulas - 7.6 Assess Your Understanding - Page 497: 11

Answer

(a) $ \frac{24}{25}$ (b) $ -\frac{7}{25}$ (c) $ \frac{2\sqrt {5}}{5}$ (d) $ -\frac{\sqrt {5}}{5}$

Work Step by Step

Given $tan\theta=\frac{4}{3}$ and $\pi\lt \theta\lt \frac{3\pi}{2}$, we have $sin\theta=-\frac{4}{5},cos\theta=-\frac{3}{5}$ and $\frac{\pi}{2}\lt \frac{\theta}{2}\lt \frac{3\pi}{4}$. (a) $sin(2\theta)=2sin\theta cos\theta=2(-\frac{4}{5})(-\frac{3}{5})=\frac{24}{25}$ (b) $cos(2\theta)=1-2sin^2(\theta)=1-2(-\frac{4}{5})^2=-\frac{7}{25}$ (c) $sin(\frac{\theta}{2})=\sqrt {\frac{1-cos\theta}{2}}=\sqrt {\frac{1+3/5}{2}}=\frac{2\sqrt {5}}{5}$ (d) $cos(\frac{\theta}{2})=-\sqrt {\frac{1+cos\theta}{2}}=-\sqrt {\frac{1-3/5}{2}}=-\frac{\sqrt {5}}{5}$
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.