Chapter 13, Problem 39SGR

To determine

To Solve : The given value is $\sin 2\theta +\cos \theta =0$

Answer to Problem 39SGR

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

Explanation of Solution

Given information :

We know that, the given equation is $\sin 2\theta +\cos \theta =0,0°\le \theta <360$

Formula Used :

  $\sin 2\theta =2\sin \theta \cos \theta$

Calculation :

The given equation is

  $\begin{array}{l}\sin 2\theta +\cos \theta =0\\ 2\sin \theta \cos \theta +\cos \theta =0\\ \cos \theta (2\sin \theta +1)=0\\ \cos \theta =0or\sin \theta =\frac{-1}{2}\\ \theta =(2n+1)\frac{\pi }{2}or\sin \theta =\sin \frac{4\pi }{3}or\sin \frac{5\pi }{3}\\ \theta =\frac{\pi }{2},\frac{3\pi }{2}or\theta =\frac{4\pi }{3}or\frac{5\pi }{3}\end{array}$