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: 9


$\sqrt 2+1$

Work Step by Step

Double -angle Theorem can be defined as: $\tan \dfrac{\theta}{2}=\pm \sqrt {\dfrac{1- \cos \theta}{1+ \cos \theta}}$ $\tan (-5 \pi/8)=\tan \dfrac{(-5 \pi/4)}{2}$ or, $=\sqrt {\dfrac{1- \cos (-5 \pi/4)}{1+ \cos (-5 \pi/4)}}$ or, $=\sqrt {\dfrac{1- \cos (2 \pi -5 \pi/4)}{1+ \cos (2 \pi-5 \pi/4)}}$ or, $=\sqrt {\dfrac{1- \cos (3 \pi/4)}{1+ \cos (3 \pi/4)}}$ or, $=\sqrt{\dfrac{2+\sqrt 2}{2-\sqrt 2}}$ or, $=\sqrt 2+1$
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