Lösung 4.4:2c
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Version vom 15:13, 22. Okt. 2008
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.
