Solution 4.4:2b

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The equation
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<center> [[Image:4_4_2b.gif]] </center>
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<math>\cos x={1}/{2}\;</math>
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{{NAVCONTENT_STOP}}
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has the solution
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<math>x={\pi }/{3}\;</math>
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in the first quadrant, and the symmetric solution
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<math>x={2\pi -\pi }/{3}\;={5\pi }/{3}\;</math>
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in the fourth quadrant.
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[[Image:4_4_2_b.gif|center]]
[[Image:4_4_2_b.gif|center]]
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Angle
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<math>{\pi }/{3}\;</math>
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Angle
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<math>{5\pi }/{3}\;</math>
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If we add multiples of
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<math>2\pi </math>
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to these two solutions, we obtain all the solutions
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<math>x={\pi }/{3}\;+2n\pi </math>
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and
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<math>x={5\pi }/{3}\;+2n\pi </math>
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where
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<math>n</math>
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is an arbitrary integer.

Revision as of 13:40, 30 September 2008

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.


Angle \displaystyle {\pi }/{3}\; Angle \displaystyle {5\pi }/{3}\;


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


\displaystyle x={\pi }/{3}\;+2n\pi and \displaystyle x={5\pi }/{3}\;+2n\pi


where \displaystyle n is an arbitrary integer.

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