Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 5 - Trigonometric Identities - Section 5.6 Half-Angle Identities - 5.6 Exercises - Page 236: 38

Answer

$$\frac{\sin158.2^\circ}{1+\cos158.2^\circ}=\tan79.1^\circ$$

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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