Mathematics

Problem

Which of the following gives the general solution of the equation

\sin x = \dfrac{1}{2}

? (Here

n\in\mathbb{Z}

.) a)

x = n\pi + \dfrac{\pi}{6}

x = 2n\pi + \dfrac{\pi}{2}\ \text{or}\ x = 2n\pi + \dfrac{3\pi}{2}

x = 2n\pi + \dfrac{\pi}{6}\ \text{or}\ x = 2n\pi + \dfrac{5\pi}{6}

x = 2n\pi + \dfrac{\pi}{3}\ \text{or}\ x = 2n\pi + \dfrac{2\pi}{3}