Mathematics - Trigonometric Equation Question with Solution | TestHub

We shall first consider values of $\theta$ between 0 $\begin{array}{rl}& \text{ and }2\pi \sin \theta =-\frac{1}{2}=-\sin \frac{\pi }{6}=\sin \left(\pi +\frac{\pi }{6}\right)\\ & \text{ or }\sin (2\pi -\pi /6)\\ & \therefore \theta =7\pi /6;11\pi /6\\ & \tan \theta =1/\sqrt{3}=\tan (\pi /6)\text{ or }\tan (\pi +\pi /6)\\ & \therefore \theta =\pi /6,7\pi /6\end{array}$ The value of $\theta$ which satisfies both the equations is $7\pi /6$ Hence the general value of $\theta$ is $2n\pi +7\pi /6$ where $\mathrm{n}\in \mathrm{I}$