Chapter 5.3, Problem 1E

To determine

To fill: The blank.

Answer to Problem 1E

General

Explanation of Solution

Given:

The _____ solution of the equation $2\cos x-1=0$ is given by $x=\frac{\pi }{3}+2n\pi ,\frac{5\pi }{3}+2n\pi$ , where n is an integer.

Calculation:

The given equation is $2\cos x-1=0$

Simplify this equation

  $\begin{array}{l}2\cos x-1=0\\ \cos x=\frac{1}{2}\end{array}$

The period of $\cos x$ is $2\pi$ . Thus, the general solution for the equation is

  $x=\frac{\pi }{3}+2n\pi ,\frac{5\pi }{3}+2n\pi$

Hence, the general solution of the equation $2\cos x-1=0$ is given by $x=\frac{\pi }{3}+2n\pi ,\frac{5\pi }{3}+2n\pi$ , where n is an integer.