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: 39

Answer

$\theta$ = 18$^{\circ}$

Work Step by Step

$\sec$(3$\theta$ + 10$^{\circ}$) = $\csc$($\theta$ + 8$^{\circ}$) $\sec$ and $\csc$ are cofunctions if the sum of the angles is 90$^{\circ}$ Therefore: (3$\theta$ + 10$^{\circ}$) + ($\theta$ + 8$^{\circ}$) = 90$^{\circ}$ 4$\theta$ + 18$^{\circ}$ = 90$^{\circ}$ 4$\theta$ = 72$^{\circ}$ $\theta$ = 18$^{\circ}$
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