Chapter 14.5, Problem 35PPS

To determine

To Solve :The given value is $4{\sin }^2\theta -1=0;180°<\theta <360°.$

Answer to Problem 35PPS

  $\theta =\frac{7\pi }{6}or\frac{11\pi }{6}$

Explanation of Solution

Given information :

We know that, the given equation is $4{\sin }^2\theta -1=0;180°<\theta <360°.$

Formula Used:

  $a^2-b^2=(a-b)(a+b)$

Calculation :

The given equation is

  $\begin{array}{l}4{\sin }^2\theta -1=0\\ (2\sin \theta -1)(2\sin \theta +1)=0\\ \sin \theta =\frac{1}{2}or\sin \theta =-\frac{1}{2}\\ As180°<\theta <360°\\ \therefore \sin \theta =-\frac{1}{2}\\ \theta =\frac{7\pi }{6}or\frac{11\pi }{6}\end{array}$