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: 3

Answer

$120/169$

Work Step by Step

We know that by the trigonometric identity $sin^2(x)+cos^2(x)=1$ that $cos(x) = \sqrt {1-(5/12)^2}$ or cos(x) is 12/13. Thus we use the identity $sin(2x)=2sin(x)cos(x)$ and get $sin(2x)=2\times12\times5/13^2$ or 60/169.
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