Lösung 4.1:2
Aus Online Mathematik Brückenkurs 1
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Version vom 14:44, 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.} |
