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: 63

Answer

Yes, there exists an angle $\theta$ with the functions values $\cos$ = 0.6 and $\sin$ = 0.8.

Work Step by Step

Using the Trigonometric Identity $\sin$$^{2}$ $\theta$ + $\cos$$^{2}$ $\theta$ = 1 we can determine if this is true. $\sin$$^{2}$ $\theta$ + $\cos$$^{2}$ $\theta$ = (-0.8)$^{2}$ + (0.6)$^{2}$ = (0.64) + (0.36) = 1.0 Since the trigonometric identity has been satisfied the angle does exist.
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