Lösung 4.1:1

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The only thing we really need to remember is that one revolution corresponds to
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Wir müssen uns eigentlich nur daran erinnern dass ein Vollwinkel 360° oder <math>2\pi</math> rad entspricht. So erhalten wir:
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360° or <math>2\pi</math> radians. Then we get:
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||a)&nbsp;&nbsp;
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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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|width="100%"|<math>\frac{1}{4}\ \text{Vollwinkel} = \frac{1}{4}\cdot 360^{\circ} = 90^{\circ}</math> and
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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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|width="100%"|<math>\frac{1}{4}\ \text{Vollwinkel} = \frac{1}{4}\cdot 2\pi\ \text{rad} = \frac{\pi}{2}\ \text{rad,}</math>
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||b)&nbsp;&nbsp;
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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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|width="100%"|<math>\frac{3}{8}\ \text{Vollwinkel} = \frac{3}{8}\cdot 360^{\circ} = 135^{\circ}</math> and
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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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||<math>\frac{3}{8}\ \text{Vollwinkel} = \frac{3}{8}\cdot 2\pi\ \text{rad} = \frac{3\pi}{4}\ \text{rad,}</math>
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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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|width="100%"|<math>-\frac{2}{3}\ \text{Vollwinkel} = -\frac{2}{3}\cdot 360^{\circ} = -240^{\circ}</math> and
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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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|width="100%"|<math>-\frac{2}{3}\ \text{Vollwinkel} = -\frac{2}{3}\cdot 2\pi\ \text{rad} = -\frac{4\pi}{3}\ \text{rad,}</math>
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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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|width="100%"|<math>\frac{97}{12}\ \text{Vollwinkel} = \frac{97}{12}\cdot 360^{\circ} = 2910^{\circ}</math> and
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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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|width="100%"|<math>\frac{97}{12}\ \text{Vollwinkel} = \frac{97}{12}\cdot 2\pi\ \text{rad} = \frac{97\pi}{6}\ \text{rad.}</math>
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Version vom 16:06, 2. Apr. 2009

Wir müssen uns eigentlich nur daran erinnern dass ein Vollwinkel 360° oder \displaystyle 2\pi rad entspricht. So erhalten wir:

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