Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.4 Equations Involving Inverse Trigonometric Functions - 6.4 Exercises - Page 286: 40


$arccos~x+2~arcsin~\frac{\sqrt{3}}{2} = \frac{-\pi}{3}$ This equation has no solutions.

Work Step by Step

$arccos~x+2~arcsin~\frac{\sqrt{3}}{2} = \frac{\pi}{3}$ $arccos~x = \frac{\pi}{3}-2~arcsin~\frac{\sqrt{3}}{2}$ $arccos~x = \frac{\pi}{3}-2~(\frac{\pi}{3})$ $arccos~x = -\frac{\pi}{3}$ Since the range of the arccos function is $[0,\pi]$, there is no value $x$ such that $arccos~x = -\frac{\pi}{3}$ Therefore, this equation has no solutions.
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