## Trigonometry (10th Edition)

Published by Pearson

# 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 &lt; $\tan$ 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$^{\circ}$ &lt; $\cot$ 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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