Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 6 - Analytic Trigonometry - Section 6.6 Double-angle and Half-angle Formulas - 6.6 Assess Your Understanding - Page 519: 30


$\dfrac{- 3}{5}$

Work Step by Step

We have: $\sin \theta=\dfrac{2}{\sqrt 5}$ and $\cos \theta=-\dfrac{1}{\sqrt 5}$ We plug these values into the following identity: $\cos (2 \ \theta)=\cos^2 \theta -\sin^2 \theta = (\dfrac{-1}{\sqrt 5})^2 -(\dfrac{2}{\sqrt 5})^2=\dfrac{- 3}{5}$
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