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: 32

Answer

$\theta$ = 40$^{\circ}$

Work Step by Step

$\cos$ $\theta$ = $\sin$ (2$\theta$ - 30$^{\circ}$) According to Cofunction Identities $\cos$ $\theta$ = $\sin$ (2$\theta$ - 30$^{\circ}$) is true only if the sum of the angles is 90$^{\circ}$. Therefore: $\theta$ + (2$\theta$ - 30$^{\circ}$) = 90$^{\circ}$ 3$\theta$ - 30$^{\circ}$ = 90$^{\circ}$ 3$\theta$ = 120$^{\circ}$ $\theta$ = 40$^{\circ}$
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