Chapter 7.5, Problem 29E

To determine

To find: all values of $\theta$by solving the equation for $0°\le \theta <360°$ .

Answer to Problem 29E

  $0°,150°,180°\text{ and 210}°$

Explanation of Solution

Given information:

  $2\sin \theta \cos \theta +\sqrt{3}\sin \theta =0$

Calculation:

The value of $\theta$ for the given equation can be evaluated as follows:

  $\begin{array}{l}2\sin \theta \cos \theta +\sqrt{3}\sin \theta =0\\ \sin \theta \cos \theta +\frac{\sqrt{3}}{2}\sin \theta =0\left[\text{Divide each side by 2}\right]\\ \sin \theta \left(\cos \theta +\frac{\sqrt{3}}{2}\right)=0\\ \sin \theta =0\text{ and cos}\theta =-\frac{\sqrt{3}}{2}\\ \theta =0°\text{ or 180}°\theta =15\text{0}°\text{ or 210}°\end{array}$

Thus the values of $\theta$ are $0°,150°,180°\text{ and 210}°$ .