Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - 7.5 Inverse Circular Functions - 7.5 Exercises: 41

Answer

$120^{o}$

Work Step by Step

Solve for radians, then convert to degrees. $y=\cos^{-1}x =\arccos x$ Domain:$[-1, 1] $ Range: $[0, \pi]$ ----------- $y$ is the number from $[0, \pi]$ such that $\displaystyle \cos y=-\frac{1}{2}.$ In quadrant I, , $\displaystyle \cos\frac{\pi}{3}=\frac{1}{2}$, In quadrant II, $\displaystyle \cos(\frac{2\pi}{3})=-\frac{1}{2}\qquad$and$\displaystyle \quad \frac{2\pi}{3}\in [0, \pi]$ , so $y =\displaystyle \frac{2\pi}{3}$ To convert radians to degrees, multiply y with $\displaystyle \frac{180^{o}}{\pi}$ $\displaystyle \theta=\frac{2\pi}{3}\cdot\frac{180^{o}}{\pi}=120^{o}$
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