Solution 4.4:2c

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m (Lösning 4.4:2c moved to Solution 4.4:2c: Robot: moved page)
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There are two angles in the unit circle,
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<center> [[Image:4_4_2c.gif]] </center>
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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.
[[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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<math>2\pi </math>,
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<math>x=0+2n\pi </math>
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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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<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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<math>x=0+n\pi </math>
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 +
 +
where
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<math>n</math>
 +
is an arbitrary integer.

Revision as of 13:47, 30 September 2008

There are two angles in the unit circle, \displaystyle x=0\text{ } 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 and \displaystyle x=\pi +2n\pi ,

where \displaystyle 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 \displaystyle n is an arbitrary integer.

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