Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 6 - Test - Page 293: 5a


$cos~ (arcsin\frac{2}{3}) = \frac{\sqrt{5}}{3}$

Work Step by Step

Let $\theta = arcsin\frac{2}{3}$ $sin~\theta = \frac{2}{3} = \frac{opp}{hyp}$ The adjacent side is $\sqrt{3^2-2^2} = \sqrt{5}$ We can find $cos~\theta$: $cos~\theta = \frac{\sqrt{5}}{3}$ Therefore, $cos~ (arcsin\frac{2}{3}) = \frac{\sqrt{5}}{3}$
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