Trigonometry (10th Edition)

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

Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.1 Inverse Circular Functions - 6.1 Exercises - Page 260: 87

Answer

$\frac{4\sqrt 6}{25}$

Work Step by Step

$\sin$(2$\cos^{-1}\frac{1}{5})$ First let $\theta$ = $\cos^{-1}$ so $cos\theta$ = $\frac{1}{5}$ Then use the Pythagorean Theorem: $A^{2}+B^{2}=C^{2}$ $\sqrt 5^{2}-\sqrt 1^{2}$ = $\sqrt 24 = 2\sqrt 6$ Find the new sin$\theta$: Sin$\theta$ = $\frac{Opposite}{Hypotenuse}$ So: Sin$\theta$ = $\frac{2\sqrt 6}{5}$ Substitue cos in the original problem with sin$\theta$ and solve: $2(\frac{2\sqrt 6}{5})(\frac{1}{5})$ = $\frac{4\sqrt 6}{25}$
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