Lösung 4.4:2c

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There are two angles in the unit circle,
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There are two angles in the unit circle, <math>x=0</math> and <math>x=\pi</math>, whose sine has a value of zero.
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<math>x=0\text{ }</math>
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and
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<math>x=\pi </math>, whose sine has a value of zero.
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[[Image:4_4_2_c.gif|center]]
[[Image:4_4_2_c.gif|center]]
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We get the full solution when we add multiples of
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We get the full solution when we add multiples of <math>2\pi</math>,
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<math>2\pi </math>,
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{{Displayed math||<math>x = 0+2n\pi\qquad\text{and}\qquad x = \pi + 2n\pi\,,</math>}}
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<math>x=0+2n\pi </math>
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where ''n'' is an arbitrary integer.
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and
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<math>x=\pi +2n\pi </math>,
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where
 
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<math>n</math>
 
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is an arbitrary integer.
 
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NOTE: Because the difference between
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Note: Because the difference between <math>0</math> and <math>\pi</math> is a half turn, the solutions are repeated every half turn and they can be summarized in one expression,
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<math>0</math>
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and
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<math>\pi </math>
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is a half turn, the solutions are repeated every half turn and they can be summarized in one expression:
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{{Displayed math||<math>x=0+n\pi\,,</math>}}
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<math>x=0+n\pi </math>
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where ''n'' is an arbitrary integer.
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where
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<math>n</math>
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is an arbitrary integer.
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Version vom 14:25, 10. 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,

Vorlage:Displayed math

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,

Vorlage:Displayed math

where n is an arbitrary integer.

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_4.4:2c“