Lösung 4.1:1

Aus Online Mathematik Brückenkurs 1

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The only thing we really need to remember is that one turn corresponds to
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The only thing we really need to remember is that one revolution corresponds to
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<math>\text{36}0^{\text{o}}</math>
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360° or <math>2\pi</math> radians. Then we get:
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or
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<math>\text{2}\pi </math>
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radians. Then we get:
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a)
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{|
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<math>\frac{1}{4}</math>
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||a)&nbsp;&nbsp;
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turn
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|width="100%"|<math>\frac{1}{4}\ \text{revolution} = \frac{1}{4}\cdot 360^{\circ} = 90^{\circ}</math> and
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<math>=\frac{1}{4}\centerdot 360^{\circ }=90^{\circ }</math>
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and
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||
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|width="100%"|<math>\frac{1}{4}\ \text{revolution} = \frac{1}{4}\cdot 2\pi\ \text{radians} = \frac{\pi}{2}\ \text{radians,}</math>
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<math>\frac{1}{4}</math>
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|-
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turn
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|height="10px"|&nbsp;
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<math>=\frac{1}{4}\centerdot 2\pi </math>
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radians
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||b)&nbsp;&nbsp;
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<math>=\frac{\pi }{2}</math>
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|width="100%"|<math>\frac{3}{8}\ \text{revolution} = \frac{3}{8}\cdot 360^{\circ} = 135^{\circ}</math> and
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radians,
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||<math>\frac{3}{8}\ \text{revolution} = \frac{3}{8}\cdot 2\pi\ \text{radians} = \frac{3\pi}{4}\ \text{radians,}</math>
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b)
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|-
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<math>\frac{3}{8}</math>
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|height="10px"|&nbsp;
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turn
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|-
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<math>=\frac{3}{8}\centerdot 360^{\circ }=135^{\circ }</math>
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||c)&nbsp;&nbsp;
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and
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|width="100%"|<math>-\frac{2}{3}\ \text{revolution} = -\frac{2}{3}\cdot 360^{\circ} = -240^{\circ}</math> and
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|-
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<math>\frac{3}{8}</math>
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turn
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|width="100%"|<math>-\frac{2}{3}\ \text{revolution} = -\frac{2}{3}\cdot 2\pi\ \text{radians} = -\frac{4\pi}{3}\ \text{radians,}</math>
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<math>=\frac{3}{8}\centerdot 2\pi </math>
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radians
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|height="10px"|&nbsp;
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<math>=\frac{3\pi }{4}</math>
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radians,
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||d)&nbsp;&nbsp;
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|width="100%"|<math>\frac{97}{12}\ \text{revolution} = \frac{97}{12}\cdot 360^{\circ} = 2910^{\circ}</math> and
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c)
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|width="100%"|<math>\frac{97}{12}\ \text{revolution} = \frac{97}{12}\cdot 2\pi\ \text{radians} = \frac{97\pi}{6}\ \text{radians.}</math>
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<math>-\frac{2}{3}</math>
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|}
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turn
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<math>=-\frac{2}{3}\centerdot 360^{\circ }=-240^{\circ }</math>
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and
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<math>-\frac{2}{3}</math>
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turn
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<math>=-\frac{2}{3}\centerdot 2\pi </math>
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radians
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<math>=-\frac{4\pi }{3}</math>
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radians,
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d)
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<math>\frac{97}{12}</math>
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turn
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<math>=\frac{97}{12}\centerdot 360^{\circ }=2910^{\circ }</math>
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and
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<math>\frac{97}{12}</math>
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turn
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<math>=\frac{97}{12}\centerdot 2\pi </math>
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radians
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<math>=\frac{97\pi }{6}</math>
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radians,
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Version vom 07:10, 3. Okt. 2008

The only thing we really need to remember is that one revolution corresponds to 360° or \displaystyle 2\pi radians. Then we get:

a)   \displaystyle \frac{1}{4}\ \text{revolution} = \frac{1}{4}\cdot 360^{\circ} = 90^{\circ} and
\displaystyle \frac{1}{4}\ \text{revolution} = \frac{1}{4}\cdot 2\pi\ \text{radians} = \frac{\pi}{2}\ \text{radians,}
 
b)   \displaystyle \frac{3}{8}\ \text{revolution} = \frac{3}{8}\cdot 360^{\circ} = 135^{\circ} and
\displaystyle \frac{3}{8}\ \text{revolution} = \frac{3}{8}\cdot 2\pi\ \text{radians} = \frac{3\pi}{4}\ \text{radians,}
 
c)   \displaystyle -\frac{2}{3}\ \text{revolution} = -\frac{2}{3}\cdot 360^{\circ} = -240^{\circ} and
\displaystyle -\frac{2}{3}\ \text{revolution} = -\frac{2}{3}\cdot 2\pi\ \text{radians} = -\frac{4\pi}{3}\ \text{radians,}
 
d)   \displaystyle \frac{97}{12}\ \text{revolution} = \frac{97}{12}\cdot 360^{\circ} = 2910^{\circ} and
\displaystyle \frac{97}{12}\ \text{revolution} = \frac{97}{12}\cdot 2\pi\ \text{radians} = \frac{97\pi}{6}\ \text{radians.}
Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_4.1:1“