Lösung 4.4:3a

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The right-hand side of the equation is a constant, so the equation is in fact a normal trigonometric equation of the type
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<center> [[Image:4_4_3a.gif]] </center>
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<math>\text{cos }x=a</math>.
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In this case, we can see directly that one solution is
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<math>x={\pi }/{6}\;</math>. Using the unit circle, it follows that
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<math>x=2\pi -{\pi }/{6}\;={11\pi }/{6}\;</math>
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is the only other solution between
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<math>0</math>
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and
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<math>\text{2}\pi </math>.
[[Image:4_4_3_a.gif|center]]
[[Image:4_4_3_a.gif|center]]
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We obtain all solutions to the equation if we add multiples of
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<math>\text{2}\pi </math>
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to the two solutions above:
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<math>x=\frac{\pi }{6}+2n\pi </math>
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and
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<math>x=\frac{11\pi }{6}+2n\pi </math>
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where
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<math>n</math>
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is an arbitrary integer.

Version vom 09:37, 1. Okt. 2008

The right-hand side of the equation is a constant, so the equation is in fact a normal trigonometric equation of the type \displaystyle \text{cos }x=a.

In this case, we can see directly that one solution is \displaystyle x={\pi }/{6}\;. Using the unit circle, it follows that \displaystyle x=2\pi -{\pi }/{6}\;={11\pi }/{6}\; is the only other solution between \displaystyle 0 and \displaystyle \text{2}\pi .

We obtain all solutions to the equation if we add multiples of \displaystyle \text{2}\pi to the two solutions above:


\displaystyle x=\frac{\pi }{6}+2n\pi and \displaystyle x=\frac{11\pi }{6}+2n\pi


where \displaystyle n is an arbitrary integer.

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_4.4:3a“