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 5.5 Double-Angle Identities - 5.5 Exercises - Page 237: 44

Answer

$\frac{tan~34^{\circ}}{2~(1-tan^2~34^{\circ})} = \frac{1}{4}~tan~68^{\circ} = 0.619$

Work Step by Step

We can use this identity: $\frac{2~tan~x}{1-tan^2~x} = tan~2x$ $\frac{tan~34^{\circ}}{2~(1-tan^2~34^{\circ})}$ $= \frac{2~tan~34^{\circ}}{4~(1-tan^2~34^{\circ})}$ $= \frac{1}{4}\cdot~\frac{2~tan~34^{\circ}}{(1-tan^2~34^{\circ})}$ $= \frac{1}{4}~tan~68^{\circ}$ $= \frac{1}{4}~(2.475)$ $= 0.619$
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