Trigonometry (10th Edition)

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

Chapter 2 - Acute Angles and Right Triangles - Section 2.2 Trigonometric Functions of Non-Acute Angles - 2.2 Exercises - Page 59: 59

Answer

False

Work Step by Step

$\cos$(2 * 45$^{\circ}$) = 2$\cos$ 45$^{\circ}$ First evaluate the value of each trigonometric statement: $\cos$ (2 * 45$^{\circ}$) = $\cos$ 90$^{\circ}$ = 0 $\cos$ 45$^{\circ}$ = $\frac{\sqrt2}{2}$ Next evaluate each side of the equation: $\tan$( 90$^{\circ}$) = 0 2 $\cos$ 45$^{\circ}$ = 2($\frac{\sqrt2}{2}$) = $\sqrt2$ Therefore: $\cos$(2 * 45$^{\circ}$) = 2$\cos$ 45$^{\circ}$ is a false statement.
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