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 6 - Analytic Trigonometry - Section 6.6 Double-angle and Half-angle Formulas - 6.6 Assess Your Understanding - Page 519: 34

Answer

$\frac{\sqrt 5+1}{2}$

Work Step by Step

1. $h(\frac{\theta}{2})=tan\frac{\theta}{2}=\frac{1-cos\theta}{sin\theta}$ 2. Use the given figures, we have $sin\theta=\frac{2}{\sqrt 5}, cos\theta=-\frac{1}{\sqrt 5}$ 3. $h(\frac{\theta}{2})=\frac{1+\frac{1}{\sqrt 5}}{\frac{2}{\sqrt 5}}=\frac{\sqrt 5+1}{2}$
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