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: 3


The positive square root should be selected. $$\tan225^\circ=\sqrt{\frac{1-\cos450^\circ}{1+\cos450^\circ}}$$

Work Step by Step

$$\tan225^\circ=\pm\sqrt{\frac{1-\cos450^\circ}{1+\cos450^\circ}}$$ Whether the positive or negative square root should be selected depends the sign of $\tan225^\circ$. $225^\circ$ lies in quadrant III. In quadrant III, both $\cos\theta\lt0$ and $\sin\theta\lt0$. Therefore, $\tan\theta=\frac{\sin\theta}{\cos\theta}\gt0$. So, $\tan225^\circ\gt0$. Thus, the positive square root should be selected. In other words, $$\tan225^\circ=\sqrt{\frac{1-\cos450^\circ}{1+\cos450^\circ}}$$
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