Trigonometrie
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(→trigonometrische Äquivalenzen) |
Current revision (21:47, 16 September 2008) (view source) (→Produkt -> Summen oder Differenz) |
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== Definitionen == | == Definitionen == | ||
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|<math>tan(\varphi) = \frac {\sin(\varphi)} {\cos(\varphi)}</math> | |<math>tan(\varphi) = \frac {\sin(\varphi)} {\cos(\varphi)}</math> | ||
|<math>cot(\varphi) = \frac {\cos(\varphi)} {\sin(\varphi)}</math> | |<math>cot(\varphi) = \frac {\cos(\varphi)} {\sin(\varphi)}</math> | ||
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== Symmetrieen == | == Symmetrieen == | ||
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|<math>\sin(\varphi+k\cdot 360^\circ) = \sin(\varphi)</math> | |<math>\sin(\varphi+k\cdot 360^\circ) = \sin(\varphi)</math> | ||
|<math>\cos(\varphi+k\cdot 360^\circ) = \cos(\varphi)</math> | |<math>\cos(\varphi+k\cdot 360^\circ) = \cos(\varphi)</math> | ||
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== trigonometrische Äquivalenzen == | == trigonometrische Äquivalenzen == | ||
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|<math>\sin(90^\circ-\varphi) = \cos(\varphi)</math> | |<math>\sin(90^\circ-\varphi) = \cos(\varphi)</math> | ||
|<math>\cos(90^\circ-\varphi) = \sin(\varphi)</math> | |<math>\cos(90^\circ-\varphi) = \sin(\varphi)</math> | ||
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== halbe Winkel == | == halbe Winkel == | ||
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|<math>\sin^2\frac\alpha 2 = \frac 1 2 (1 - \cos\alpha)</math> | |<math>\sin^2\frac\alpha 2 = \frac 1 2 (1 - \cos\alpha)</math> | ||
|<math>1 - \cos 2\alpha = 2 \sin^2\alpha</math> | |<math>1 - \cos 2\alpha = 2 \sin^2\alpha</math> | ||
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|<math>\tan^2\frac\alpha 2 = \frac {1 - \cos\alpha}{1 + \cos\alpha}</math> | |<math>\tan^2\frac\alpha 2 = \frac {1 - \cos\alpha}{1 + \cos\alpha}</math> | ||
|} | |} | ||
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| + | == Summen und Differenzen -> Produkt == | ||
| + | |||
| + | <math>\sin\alpha + \sin\beta = 2 \sin\frac{\alpha+\beta} 2 \cos\frac{\alpha-\beta} 2</math> | ||
| + | |||
| + | <math>\sin\alpha - \sin\beta = 2 \cos\frac{\alpha+\beta} 2 \sin\frac{\alpha-\beta} 2</math> | ||
| + | |||
| + | <math>\cos\alpha + \cos\beta = 2 \cos\frac{\alpha+\beta} 2 \cos\frac{\alpha-\beta} 2</math> | ||
| + | |||
| + | <math>\cos\alpha - \cos\beta = -2 \sin\frac{\alpha+\beta} 2 \sin\frac{\alpha-\beta} 2</math> | ||
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| + | == Produkt -> Summen oder Differenz == | ||
| + | |||
| + | <math>2\,\sin\alpha \sin\beta = \cos(\alpha-\beta} - \cos(\alpha+\beta)</math> | ||
| + | |||
| + | <math>2\,\cos\alpha \cos\beta = \cos(\alpha-\beta} + \cos(\alpha+\beta)</math> | ||
| + | |||
| + | <math>2\,\sin\alpha \cos\beta = \sin(\alpha-\beta} + \sin(\alpha+\beta)</math> | ||
| + | |||
[[category:Mathematik]] | [[category:Mathematik]] | ||
Current revision
Contents |
Definitionen
Symmetrieen
trigonometrische Äquivalenzen
Additionstheoreme
doppelte Winkel
halbe Winkel
Summen und Differenzen -> Produkt
Produkt -> Summen oder Differenz
