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 242: 38



Work Step by Step

$$\frac{\sin158.2^\circ}{1+\cos158.2^\circ}$$ From the half-angle identity for tangents: $$\frac{\sin A}{1+\cos A}=\tan\frac{A}{2}$$ We can apply the identity to the given expression with $A=158.2^\circ$. $$\frac{\sin158.2^\circ}{1+\cos158.2^\circ}=\tan\frac{158.2^\circ}{2}$$ $$\frac{\sin158.2^\circ}{1+\cos158.2^\circ}=\tan79.1^\circ$$
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