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: 67

Answer

$sec$($\theta$ + 180$^{\circ}$) is positive in the interval (90$^{\circ}$,180$^{\circ}$).

Work Step by Step

$\theta$ is in the interval (90$^{\circ}$,180$^{\circ}$) Therefore: $\theta$ exists in Quadrant II. Therefore, $\theta$ + 180$^{\circ} $exists in Quadrant IV. All trigonometric functions are negative, in Quadrant IV, except for $\sec$ and $\cos$. Therefore $sec$($\theta$ + 180$^{\circ}$) is positive in the interval (90$^{\circ}$,180$^{\circ}$).
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