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: 4


The negative square root should be selected. $$\sin(-10^\circ)=-\sqrt{\frac{1-\cos(-20^\circ)}{2}}$$

Work Step by Step

$$\sin(-10^\circ)=\pm\sqrt{\frac{1-\cos(-20^\circ)}{2}}$$ Whether the positive or negative square root should be selected depends the sign of $\sin(-10^\circ)$. The position of angle $-10^\circ$ collides with that of angle $350^\circ$. So we can consider $\sin(-10^\circ)=\sin350^\circ$ $350^\circ$ lies in quadrant IV. In quadrant IV, $\sin\theta\lt0$. Thus, $\sin350^\circ=\sin(-10^\circ)\lt0$. Thus, the negative square root should be selected. In other words, $$\sin(-10^\circ)=-\sqrt{\frac{1-\cos(-20^\circ)}{2}}$$
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