Which of the following gives the general solution of the equation

MATHEMATICS · Single correct · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

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

? (Here

n\in\mathbb{Z}

.) (a)

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

(b)

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

(c)

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

(d)

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