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 9 - Analytic Geometry - Section 9.5 Rotation of Axes; General Form of a Conic - 9.5 Assess Your Understanding - Page 698: 3


$\sin (\dfrac{\theta}{2}) =\sqrt {\dfrac{1-\cos \theta}{2}}$

Work Step by Step

We know that the half-angle formula for $\sin$ is $\sin (\dfrac{x}{2}) = \pm \sqrt {\dfrac{1-\cos x}{2}}$ Since the angle is acute, we will write it as: $\sin (\dfrac{\theta}{2}) =\sqrt {\dfrac{1-\cos \theta}{2}}$
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