From Förberedande kurs i matematik 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.

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

\displaystyle x = \frac{\pi}{3}+2n\pi\qquad\text{and}\qquad x = \frac{5\pi }{3}+2n\pi\,,

where n is an arbitrary integer.