Trigonometry (10th Edition)

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

Chapter 1 - Trigonometric Functions - Section 1.4 Using the Definitions of the Trigonometric Functions - 1.4 Exercises: 103

Answer

$\theta=3^{\circ}$

Work Step by Step

1. Cosecant and sine are reciprocals $\csc\theta=\frac{1}{\sin\theta}$ 2. Rewrite cosencant as a sine $\sin(4\theta +2^{\circ})=\sin(3\theta+5^{\circ})$ 3.Since the sine values are equal, the angles themselves must be equal. $4\theta -3\theta= 5-2$ $\theta=3^{\circ}$
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