Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 5 - Trigonometric Identities - Section 5.6 Half-Angle Identities - 5.6 Exercises - Page 243: 44



Work Step by Step

$$\pm\sqrt{\frac{1-\cos\frac{3\theta}{5}}{2}}$$ From the half-angle identity for sine: $$\pm\sqrt{\frac{1-\cos A}{2}}=\sin\frac{A}{2}$$ We can apply the identity to the given expression with $A=\frac{3\theta}{5}$. $$\pm\sqrt{\frac{1-\cos\frac{3\theta}{5}}{2}}=\sin\frac{\frac{3\theta}{5}}{2}$$ $$\pm\sqrt{\frac{1-\cos\frac{3\theta}{5}}{2}}=\sin\frac{3\theta}{10}$$
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