Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 6 - 6.6 - Inverse Trigonometric Functions - 6.6 Exercises - Page 485: 76


$\arccos \dfrac{x}{6}=\arcsin \dfrac{\sqrt {36-x^2}}{6}$

Work Step by Step

Consider $\theta=\arcsin \dfrac{\sqrt {36-x^2}}{6}$ We can see that $\sqrt {36-x^2}$ is a positive quanity and $\theta$ must lie in the first quadrant. So, we have: $\cos \theta=\dfrac{x}{6} $ and $\theta =\arccos \dfrac{x}{6} $ and $\arccos \dfrac{x}{6}=\arcsin \dfrac{\sqrt {36-x^2}}{6}$
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