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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: 04
$\begin{array}{l}
\text{Gegeben:}\\\text{Winkel} \qquad \alpha \qquad [^{\circ}] \\
\\ \text{Gesucht:} \\\text{Sinus alpha} \qquad sin \alpha \qquad [] \\
\\ sin \alpha = tan\alpha \cdot cos \alpha\\ \textbf{Gegeben:} \\ \alpha=45^{\circ} \qquad \\ \\ \textbf{Rechnung:} \\
sin \alpha = tan\alpha \cdot cos \alpha \\
\alpha=45^{\circ}\\
sin \alpha = tan45^{\circ} \cdot cos 45^{\circ}\\\\sin \alpha=0,707
\\\\\\ \small \begin{array}{|l|} \hline alpha=\\ \hline 45 ° \\ \hline 2,7\cdot 10^{3} \text{'} \\ \hline 1,62\cdot 10^{5} \text{''} \\ \hline 50 gon \\ \hline 0,785 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline sinalpha=\\ \hline 0,707 rad \\ \hline 707 mrad \\ \hline 40,5 ^\circ \\ \hline 2,43\cdot 10^{3} \text{'} \\ \hline 1,46\cdot 10^{5} \text{'''} \\ \hline \end{array} \end{array}$