Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - 7.4 Double-Angle and Half-Angle Identities - 7.4 Exercises - Page 693: 51



Work Step by Step

Use the half-angle formula, $\tan\frac{u}{2}=\frac{1-\cos u}{\sin u}$. $\tan 195^\circ$ $=\tan \frac{390^\circ}{2}$ $=\frac{1-\cos 390^\circ}{\sin 390^\circ}$ $=\frac{1-\cos 30^\circ}{\sin 30^\circ}$ $=\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}$ $=\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}*\frac{2}{2}$ $=\frac{2-\sqrt{3}}{1}$ $=2-\sqrt{3}$
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