Trigonometry (10th Edition)

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

Chapter 6 - Test - Page 288: 19a

Answer

$x = \frac{4}{5}$

Work Step by Step

Let $\theta = arctan~\frac{4}{3}$ Then $tan~\theta = \frac{4}{3} = \frac{opp}{adj}$ If the opposite side is 4 and the adjacent side is 3, then the hypotenuse is $\sqrt{4^2+3^2} = 5$ Then $sin~\theta = \frac{4}{5}$ Therefore, $arcsin~\frac{4}{5} = \theta = arctan ~\frac{4}{3}$ $x = \frac{4}{5}$
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