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: 64

Answer

No, there does not exist an angle with the function values $\cos$$\theta$ = $\frac{2}{3}$ and $\sin$$\theta$ = $\frac{3}{4}$.

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}$ $\theta$ = ($\frac{3}{4}$)$^{2}$ + ($\frac{2}{3}$)$^{2}$ = ($\frac{9}{16}$) + ($\frac{4}{9}$) = $\frac{145}{144}$ $\frac{145}{144}$ $\ne$ 1 Since the trigonometric identity has been not been satisfied the angle does not exist.
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