## Trigonometry (10th Edition)

Published by Pearson

# Chapter 2 - Acute Angles and Right Triangles - Section 2.1 Trigonometric Functions of Acute Angles - 2.1 Exercises: 45

#### Answer

$\tan$ 41$^{\circ}$ $\lt$ $\cot$41$^{\circ}$ is true.

#### Work Step by Step

$\tan$ 41 &lt; $\cot$ 41 We must first get the inequality in terms of $\tan$ $\cot$ $A$ = $\tan$ (90$^{\circ}$ - $A$) Therefore: $\cot$ 41 = $\tan$(90$^{\circ}$ - 41$^{\circ}$) $\cot$ 28 = $\tan$ 49$^{\circ}$ The inequality could be rewritten: $\tan$ 41 &lt; $\cot$ 49 From 0$^{\circ}$ to 90$^{\circ}$, as the angle increases, the $tangent$ of the angle increases. Therefore: $\tan$ 41$^{\circ}$ $\lt$ $\tan$ 49$^{\circ}$ is true. Therefore: $\tan$ 41$^{\circ}$ $\lt$ $\cot$41$^{\circ}$ is true.

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