Aus Online Mathematik Brückenkurs 1

There are two angles in the unit circle, \displaystyle x=0 and \displaystyle x=\pi, whose sine has a value of zero.

We get the full solution when we add multiples of \displaystyle 2\pi,

\displaystyle x = 0+2n\pi\qquad\text{and}\qquad x = \pi + 2n\pi\,,

where n is an arbitrary integer.

Note: Because the difference between \displaystyle 0 and \displaystyle \pi is a half turn, the solutions are repeated every half turn and they can be summarized in one expression,

\displaystyle x=0+n\pi\,,

where n is an arbitrary integer.