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: 43

Answer

$120^{o}$

Work Step by Step

Solve for radians, then convert to degrees. $y=\cot^{-1}x$ Domain: $(-\infty, \infty) $ Range: $(0, \pi)$ ----------- $y$ is the number from $(0, \pi)$ such that $\displaystyle \cot y=-\frac{\sqrt{3}}{3}$ In quadrant I, $\displaystyle \cot(\frac{\pi}{3})=\frac{\sqrt{3}}{3}$, in quadrant II, $\displaystyle \cot(\frac{2\pi}{3})=-\frac{\sqrt{3}}{3}$ $\cot$($\displaystyle \frac{2\pi}{3})=-\sqrt{3}\quad$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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