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 241: 2


The positive square root should be selected. $$\cos58^\circ=\sqrt{\frac{1+\cos116^\circ}{2}}$$

Work Step by Step

$$\cos58^\circ=\pm\sqrt{\frac{1+\cos116^\circ}{2}}$$ Whether the positive or negative square root should be selected depends the sign of $\cos58^\circ$. $58^\circ$ lies in quadrant I. In quadrant I, $\cos\theta\gt0$. Therefore, $\cos58^\circ\gt0$. Thus, the positive square root should be selected. In other words, $$\cos58^\circ=\sqrt{\frac{1+\cos116^\circ}{2}}$$
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