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: 101

Answer

$\theta=2^{\circ}$

Work Step by Step

1. Tangent and cotangent are reciprocals $\tan\theta=\frac{1}{\cot 5\theta}$ 2. Rewrite cotangent as a tengent $\tan(3\theta -4^{\circ})=\tan(5\theta-8^{\circ})$ 3.Since the tangent values are equal, the angles themselves must be equal. $5\theta -3\theta= -4+8$ $2\theta=4$ $\theta=2^{\circ}$
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