trigonometry equation

Submitted by gokudeep on Sun, 04/18/2010 - 14:09.

i didn't understood this topic please explain it
1.)
$sinx \ge -\frac{1}{2}$
and the answer is

$-\frac{\pi}{6}+2n\pi\le x \le \frac{7\pi}{6}+2n\pi$

where n belongs to integers
2.)
similarly for below
$cosx \ge \frac{1}{2}$
and the answer is
$2n\pi-\frac{\pi}{3}\le x \le 2n\pi+\frac{\pi}{3}$

where n belongs to integers
Is there any general methodology for this please help me