Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 7 - Section 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas - 7.3 Exercises - Page 561: 51

Answer

$\frac{7}{25}$

Work Step by Step

Step 1. As $\theta$ is in Quadrant III, we have $\pi\lt\theta\lt\frac{3\pi}{2}$ and $2\pi\lt2\theta\lt3\pi$ which means that $cos2\theta$ can be both positive or negative. Step 2. Given $sin\theta=-\frac{3}{5}$, use the Double-Angle Formula, we have $cos2\theta=1-2sin^2\theta=1-2\times(-\frac{3}{5})^2=1-\frac{2\times9}{25}=\frac{7}{25}$
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