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Lösung 4.4:2f

Aus Online Mathematik Brückenkurs 1

(Unterschied zwischen Versionen)
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K (Lösning 4.4:2f moved to Solution 4.4:2f: Robot: moved page)
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{{NAVCONTENT_START}}
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Using the unit circle shows that the equation
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<center> [[Image:4_4_2f.gif]] </center>
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<math>\text{cos 3}x=-\frac{1}{\sqrt{2}}</math>
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{{NAVCONTENT_STOP}}
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has two solutions for
 +
<math>0\le \text{3}x\le \text{2}\pi </math>,
 +
 
 +
 
 +
<math>3x=\frac{\pi }{2}+\frac{\pi }{4}=\frac{3\pi }{4}</math>
 +
and
 +
<math>3x=\pi +\frac{\pi }{4}=\frac{5\pi }{4}</math>
[[Image:4_4_2_f.gif|center]]
[[Image:4_4_2_f.gif|center]]
 +
 +
We obtain the other solutions by adding multiples of
 +
<math>2\pi </math>,
 +
 +
 +
<math>3x=\frac{3\pi }{4}+2n\pi </math>
 +
and
 +
<math>3x=\frac{5\pi }{4}+2n\pi </math>
 +
 +
 +
i.e.
 +
 +
 +
<math>x=\frac{\pi }{4}+\frac{2}{3}n\pi </math>
 +
and
 +
<math>x=\frac{5\pi }{12}+\frac{2}{3}n\pi </math>
 +
 +
 +
where
 +
<math>n</math>
 +
is an arbitrary integer.

Version vom 08:57, 1. Okt. 2008

Using the unit circle shows that the equation cos 3x=−12 has two solutions for 03x2,


3x=2+4=43 and 3x=+4=45

We obtain the other solutions by adding multiples of 2,


3x=43+2n and 3x=45+2n


i.e.


x=4+32n and x=125+32n


where n is an arbitrary integer.

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