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: 3

Answer

$\sin$46$^{\circ}$ $\lt$ $\cos $46$^{\circ}$ is false.

Work Step by Step

$\sin$46 < $\cos$46 We must first get the inequality in terms of $\sin$ $\cos$ $A$ = $\sin$ (90$^{\circ}$ - $A$) Therefore: $\cos$ 46 = $\sin$(90$^{\circ}$ - 46$^{\circ}$) $\cos$ 46 = $\sin $44$^{\circ}$ The inequality could be rewritten: $\sin $46 < $\sin$44 From 0$^{\circ}$ to 90$^{\circ}$, as the angle increases, so does the $sine$ of the angle. Therefore: $\sin$46$^{\circ}$ $\lt$ $\sin $44$^{\circ}$ is false. Therefore: $\sin$46$^{\circ}$ $\lt$ $\cos $46$^{\circ}$ is false.
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