Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 5 - Section 5.5 - Additional Identities - 5.5 Problem Set - Page 311: 12



Work Step by Step

$\alpha =\tan^{-1} \dfrac{3}{4}$ $\tan{\alpha} = \dfrac{3}{4}$ $\sec{\alpha} =\sqrt{1+\tan^2{\alpha}} = \dfrac{5}{4}$ $\cos{\alpha} =\dfrac{1}{\sec{\alpha}} = \dfrac{4}{5}$ $\sin{\alpha} = \sqrt{1-\cos^2{\alpha}} = \dfrac{3}{5}$ $\sin{2\alpha} =2 \sin{\alpha} \cos{\alpha} =2\times \dfrac{3}{5} \times \dfrac{4}{5} = \dfrac{24}{25}$
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