Aus Online Mathematik Brückenkurs 1

The equation \displaystyle \cos x={1}/{2}\; has the solution \displaystyle x={\pi }/{3}\; in the first quadrant, and the symmetric solution \displaystyle x={2\pi -\pi }/{3}\;={5\pi }/{3}\; in the fourth quadrant.

Angle \displaystyle {\pi }/{3}\; Angle \displaystyle {5\pi }/{3}\;

If we add multiples of \displaystyle 2\pi to these two solutions, we obtain all the solutions

\displaystyle x={\pi }/{3}\;+2n\pi and \displaystyle x={5\pi }/{3}\;+2n\pi

where \displaystyle n is an arbitrary integer.