sin x > - 1 / 2 ; arcsin ( - 1 / 2 ) + 2 * pi * n < x < pi - arcsin ( - 1 / 2 ) + 2 * pi * n ;7 * pi / 6 + 2 * pi * n < x < pi - 7 * pi / 6 + 2 * pi * n ;7 * pi / 6 + 2 * pi * n < x < - pi / 6 + 2 * pi * n ; - pi / 6 + 2 * pi * n < x < 7 * pi / 6 + 2 * pi * n.