Lösung 4.1:2

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If we use the mnemonic that one turn is 360° or <math>2\pi</math> radians, we can derive a formula for the transformation from degrees to radians. Because
If we use the mnemonic that one turn is 360° or <math>2\pi</math> radians, we can derive a formula for the transformation from degrees to radians. Because
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{{Displayed math||<math>360\cdot 1^{\circ } = 2\pi\ \text{radians}</math>}}
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{{Abgesetzte Formel||<math>360\cdot 1^{\circ } = 2\pi\ \text{radians}</math>}}
this gives
this gives
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{{Displayed math||<math>1^{\circ} = \frac{2\pi}{360}\ \text{radians} = \frac{\pi}{180}\ \text{radians.}</math>}}
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{{Abgesetzte Formel||<math>1^{\circ} = \frac{2\pi}{360}\ \text{radians} = \frac{\pi}{180}\ \text{radians.}</math>}}
Now we can start transforming the angles:
Now we can start transforming the angles:

Version vom 08:47, 22. Okt. 2008

If we use the mnemonic that one turn is 360° or \displaystyle 2\pi radians, we can derive a formula for the transformation from degrees to radians. Because

\displaystyle 360\cdot 1^{\circ } = 2\pi\ \text{radians}

this gives

\displaystyle 1^{\circ} = \frac{2\pi}{360}\ \text{radians} = \frac{\pi}{180}\ \text{radians.}

Now we can start transforming the angles:


a)   \displaystyle 45^{\circ} = 45\cdot 1^{\circ} = 45\cdot\frac{\pi}{180}\ \text{radians} = \frac{\pi}{4}\ \text{radians,}
 
b)   \displaystyle 135^{\circ } = 135\cdot 1^{\circ} = 135\cdot\frac{\pi}{180}\ \text{radians} = \frac{3\pi}{4}\ \text{radians,}
 
c)   \displaystyle -63^{\circ} = -63\cdot 1^{\circ} = -63\cdot\frac{\pi}{180}\ \text{radians} = -\frac{7\pi}{20}\ \text{radians,}
 
d) \displaystyle 270^{\circ} = 270\cdot 1^{\circ} = 270\cdot\frac{\pi}{180}\ \text{radians} = \frac{3\pi}{2}\ \text{radians.}
Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_4.1:2“