Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 5 - Section 5.5 - Trigonometric Equations - Exercise Set - Page 704: 102


The given equation has no solutions.

Work Step by Step

We have to solve the equation as follows: $\cos x-5=3\cos x+6$ Arrange the given equation in such a way that the cosine functions are on one side and the real numbers are on the other as follows: $\begin{align} & \cos x-3\cos x=6+5 \\ & -2\cos x=11 \\ & \cos x=\frac{-11}{2} \end{align}$ Thus, the cosine value of all the numbers always lies in the interval $\left[ -1,1 \right]$; the cosine value cannot be less than 1. So, $\cos x=\frac{-11}{2}$ is not possible.
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