Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 2 - Acute Angles and Right Triangles - Section 2.2 Trigonometric Functions of Non-Acute Angles - 2.2 Exercises: 65

Answer

$cos$$\frac{\theta}{2}$ is positive in the interval (90$^{\circ}$,180$^{\circ}$).

Work Step by Step

$\theta$ is in the interval (90$^{\circ}$,180$^{\circ}$) Therefore: $\frac{\theta}{2}$ $\leq$ 90$^{\circ}$ Therefore, $\frac{\theta}{2}$ exists in Quadrant 1. All trigonometric functions are positive in Quadrant 1. Therefore $cos$$\frac{\theta}{2}$ is positive in the interval (90$^{\circ}$,180$^{\circ}$).
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