If \sin \theta \geq \dfrac{\sqrt{3} }{2}, determine the domain of \theta in a unit circle

#### Question

#### Answer

If \sin \theta \geq \dfrac{\sqrt{3} }{2}, \theta is in the domain of

\dfrac{\pi}{3} \leq \theta \leq \dfrac{2\pi}{3}

First construct the angle \dfrac{\pi}{3} in the unit circle

And then construct the angle of \dfrac{2\pi}{3}

The domain of \theta is the area between the two angles