Trigonometry (10th Edition)

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

Chapter 2 - Acute Angles and Right Triangles - Section 2.1 Trigonometric Functions of Acute Angles - 2.1 Exercises: 46

Answer

$\cot$ 30$^{\circ}$ $\lt$ $\tan$ 40$^{\circ}$ is false.

Work Step by Step

$\cot$ 30 < $\tan$ 40 We must first get the inequality in terms of $\cot$ $\tan$ $A$ = $\cot$ (90$^{\circ}$ - $A$) Therefore: $\tan$ 40 = $\cot$(90$^{\circ}$ - 41$^{\circ}$) $\tan$ 40 = $\cot$ 50$^{\circ}$ The inequality could be rewritten: $\cot$ 30$^{\circ}$ < $\cot$ 50$^{\circ}$ From 0$^{\circ}$ to 90$^{\circ}$, as the angle increases, the $cotangent$ of the angle decreases. Therefore: $\cot$ 30$^{\circ}$ $\lt$ $\cot$ 50$^{\circ}$ is false. Therefore: $\cot$ 30$^{\circ}$ $\lt$ $\tan$ 40$^{\circ}$ is false.
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