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: 44

Answer

$\cos$ 28$^{\circ}$ $\lt$ $\sin $28$^{\circ}$ is false.

Work Step by Step

$\cos$ 28 < $\sin$ 28 We must first get the inequality in terms of $\cos$ $\sin$ $A$ = $\cos$ (90$^{\circ}$ - $A$) Therefore: $\sin$ 28 = $\cos$(90$^{\circ}$ - 28$^{\circ}$) $\sin$ 28 = $\cos$ 62$^{\circ}$ The inequality could be rewritten: $\cos$ 28 < $\cos$ 62 From 0$^{\circ}$ to 90$^{\circ}$, as the angle increases, the $cosine$ of the angle decreases. Therefore: $\cos$ 28$^{\circ}$ $\lt$ $\cos$ 62$^{\circ}$ is false. Therefore: $\cos$ 28$^{\circ}$ $\lt$ $\sin $28$^{\circ}$ is false.
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