## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

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

#### Answer

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

#### 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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