Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.7 Apply Double-Angle and Half-Angle Formulas - 14.7 Exercises - Skill Practice - Page 959: 17


$\dfrac{4}{5}$ and $\dfrac{-3}{5}$ and $-\dfrac{4}{3}$

Work Step by Step

$\cos a= \dfrac{1}{\sec a}=- \dfrac{1}{\sqrt {1+\tan^2 a}}=-\dfrac{1}{\sqrt {1+2^2}}=-\dfrac{\sqrt 5}{5}$ $\sin 2a=2 \sin a \cos a = 2 (-\dfrac{ 2\sqrt 5}{5}) (-\dfrac{\sqrt 5}{5})=\dfrac{4}{5}$ $\cos 2a =\cos^2 a-\sin^2 a=(-\dfrac{\sqrt 5}{5})^2 - (-\dfrac{ 2\sqrt 5}{5})^2=\dfrac{1}{5}-\dfrac{4}{5}=\dfrac{-3}{5}$ $\tan 2a =\dfrac{\sin 2a}{\cos 2a}=\dfrac{4/5}{-3/5}=-\dfrac{4}{3}$
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