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$ sin \alpha = \sqrt{1 - cos^{2} \alpha } $
$ cos \alpha = \sqrt{1 - sin^{2} \alpha } $
$ tan \alpha = \frac{sin \alpha }{cos \alpha } $
$ sin \alpha = tan\alpha \cdot cos \alpha $
$ cos \alpha = \frac{sin \alpha }{tan \alpha } $
Geometrie-Trigonometrie-Umrechnungen
$ sin^{2} \alpha + cos^{2} \alpha = 1 $
$sin \alpha = \sqrt{1 - cos^{2} \alpha }$
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$cos \alpha = \sqrt{1 - sin^{2} \alpha }$
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$tan \alpha = \frac{sin \alpha }{cos \alpha }$
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$sin \alpha = tan\alpha \cdot cos \alpha$
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$cos \alpha = \frac{sin \alpha }{tan \alpha }$
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Beispiel Nr: 05
$\begin{array}{l}
\text{Gegeben:}\\\text{Winkel} \qquad \alpha \qquad [^{\circ}] \\
\\ \text{Gesucht:} \\\text{Sinus alpha} \qquad sin \alpha \qquad [] \\
\\ sin \alpha = \sqrt{1 - cos^{2} \alpha }\\ \textbf{Gegeben:} \\ \alpha=120^{\circ} \qquad \\ \\ \textbf{Rechnung:} \\
sin \alpha = \sqrt{1 - cos^{2} \alpha } \\
\alpha=120^{\circ}\\
sin 120^{\circ} = \sqrt{1 - cos^{2} 120^{\circ} }\\\\sin 120^{\circ}=0,866
\\\\\\ \small \begin{array}{|l|} \hline alpha=\\ \hline 120 ° \\ \hline 7,2\cdot 10^{3} \text{'} \\ \hline 4,32\cdot 10^{5} \text{''} \\ \hline 133\frac{1}{3} gon \\ \hline 2,09 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline sinalpha=\\ \hline 0,866 rad \\ \hline 866 mrad \\ \hline 49,6 ^\circ \\ \hline 2,98\cdot 10^{3} \text{'} \\ \hline 1,79\cdot 10^{5} \text{'''} \\ \hline \end{array} \end{array}$