Chapter 13, Problem 38SGR

To determine

To Solve : The given value is $4{\cos }^2\theta -1=0;0\le \theta <2\pi$

Answer to Problem 38SGR

  $\theta =\frac{\pi }{3},\frac{5\pi }{3}or\theta =\frac{2\pi }{3},\frac{4\pi }{3}$

Explanation of Solution

Given information :

We know that, the given equation is $4{\cos }^2\theta -1=0$

Formula Used :

  $\cos \frac{\pi }{3}=\frac{1}{2}$

Calculation :

The given equation is

  $\begin{array}{l}4{\cos }^2\theta -1=0\\ {\cos }^2\theta =\frac{1}{4}\\ \cos \theta =\pm \frac{1}{2}\\ \cos \theta =\frac{1}{2}or\cos \theta =-\frac{1}{2}\\ \theta =\frac{\pi }{3},\frac{5\pi }{3}or\theta =\frac{2\pi }{3},\frac{4\pi }{3}\end{array}$