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: 10


$\dfrac{\sqrt{2-\sqrt 3}}{2}$

Work Step by Step

Double -angle Theorem can be defined as: $\sin \dfrac{\theta}{2}=\pm \sqrt {\dfrac{1- \cos \theta}{2}}$ $\sin (-\dfrac{11 \pi}{2})=\sin (-\dfrac{11 \pi}{2}+2 \pi)=\sin (\dfrac{ \pi}{12})$ and $\sin (\dfrac{ \pi}{12})=\sin (\dfrac{ \pi/6}{2})$ or, $=\pm \sqrt {\dfrac{1- \cos (\pi/6)}{2}}$ or, $= \sqrt {\dfrac{1-(-\sqrt 3/2)}{2}}$ or, $=\dfrac{\sqrt{2-\sqrt 3}}{2}$
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