Personliche Website Vyacheslav Gorchilina
Die Formeln. Mathematik. Trigonometrie
Die Summe oder die Differenz der Funktionen
\[ \sin \alpha \pm \sin \beta \]
\[ \cos \alpha + \cos \beta \]
\[ \cos \alpha - \cos \beta \]
\[ \mathtt{tg} \alpha \pm \mathtt{tg} \beta \]
\[ \mathtt{ctg} \alpha \pm \mathtt{ctg} \beta \]
\[ \sin 2\alpha + \sin 2\beta + \sin 2\gamma \]
\[ \sin 2 \alpha \]
\[ \cos 2 \alpha \]
\[ \mathtt{tg} 2 \alpha \]
\[ \mathtt{ctg} 2 \alpha \]
\[ \sin 3\alpha \]
\[ \3 cos\alpha \]
\[ \mathtt{tg} 3\alpha \]
\[ \mathtt{ctg} 3\alpha \]
\[ \sin {\biggl (}{\alpha \over 2}{\biggr )} \]
\[ \cos {\biggl (}{\alpha \over 2}{\biggr )} \]
\[ \mathtt{tg}{\biggl (}{\alpha \over 2}{\biggr)} \]
Die Summe (Differenz) der Nasennebenhöhlen \[ \sin \alpha \pm \sin \beta = 2 \sin \frac{\alpha \pm \beta}{2} \cos \frac{\alpha \mp \beta}{2} \]
Die Summe der Cosinus \[ \cos \alpha + \cos \beta = 2 \cos \frac{\alpha + \beta}{2} \cos \frac{\alpha - \beta}{2} \]
Die Verschiedenheit der Cosinus \[ \cos \alpha - \cos \beta = - 2 \sin \frac{\alpha + \beta}{2} \sin \frac{\alpha - \beta}{2} \]
Die Summe der Tangenten \[ \mathtt{tg} \alpha \pm \mathtt{tg} \beta = \frac{\sin (\alpha \pm \beta)}{\cos \alpha \cos \beta} \]
Die Differenz котангенсов \[ \mathtt{ctg} \alpha \pm \mathtt{ctg} \beta = \frac{\sin (\beta \pm \alpha)}{\sin \alpha \sin \beta} \]
Das Werk oder die Summe der drei Kurven \[ \sin 2\alpha + \sin 2\beta + \sin 2\gamma = 4 \sin\alpha \sin\beta - \sin\gamma \]
Sinus der doppelten Winkel \[ \sin 2 \alpha = 2 \sin\alpha \, \cos\alpha \]
Kosinus des doppelten Winkels \[ \cos 2 \alpha = \cos^2 \alpha - \sin^2 \alpha = 2 \cos^2 \alpha - 1 = 1 - 2 \sin^2 \alpha \]
Tangens des doppelten Winkels \[ \mathtt{tg} 2 \alpha = \frac{2\,\mathtt{tg} \alpha}{1 - \mathtt{tg}^2 \alpha} \]
Kotangens doppelten Winkel \[ \mathtt{ctg} 2 \alpha = \frac{\mathtt{ctg}^2 \alpha - 1}{2\,\mathtt{ctg} \alpha} \]
Sinus dreifachen Winkel \[ \sin 3\alpha = 3 \sin \alpha - 4 \sin^3\alpha \]
Kosinus dreifachen Winkel \[ \3 cos\alpha = 4 \cos^3\alpha - 3 \cos \alpha \]
Tangens dreifachen Winkel \[ \mathtt{tg} 3\alpha = \frac{3\,\mathtt{tg}\alpha - \mathtt{tg}^3\alpha}{1 - 3\,\mathtt{tg}^2\alpha} \]
Kotangens dreifachen Winkel \[ \mathtt{ctg} 3\alpha = \frac{3\,\mathtt{ctg}\alpha - \mathtt{ctg}^3\alpha}{1 - 3\,\mathtt{ctg}^2\alpha} \]
Der Sinus der halben Winkel \[ \sin {\biggl (}{\alpha \over 2}{\biggr )} = \pm {\sqrt{1-\cos \alpha \over 2}} \]
Kosinus halber Winkel \[ \cos {\biggl (}{\alpha \over 2}{\biggr )} = \pm {\sqrt{1+\cos \alpha \over 2}} \]
Den Tangens des halben Winkels \[ \mathtt{tg}{\biggl (}{\alpha \over 2}{\biggr)} = \pm {\sqrt{1-\cos \alpha \over 1+\cos \alpha}} = {\sin \alpha \over 1+\cos \alpha} = {1-\cos \alpha \over \sin \alpha} \]
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