Geometrie-Trigonometrie-Umrechnungen

$ sin^{2} \alpha + cos^{2} \alpha = 1 $
$sin \alpha = \sqrt{1 - cos^{2} \alpha }$
1 2 3 4 5
$cos \alpha = \sqrt{1 - sin^{2} \alpha }$
1 2 3 4 5
$tan \alpha = \frac{sin \alpha }{cos \alpha }$
1 2 3 4 5 6
$sin \alpha = tan\alpha \cdot cos \alpha$
1 2 3 4
$cos \alpha = \frac{sin \alpha }{tan \alpha }$
1 2 3 4
Beispiel Nr: 03
$\begin{array}{l} \text{Gegeben:}\\\text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \\ \text{Gesucht:} \\\text{Kosinus alpha} \qquad cos \alpha \qquad [] \\ \\ cos \alpha = \sqrt{1 - sin^{2} \alpha }\\ \textbf{Gegeben:} \\ \alpha=45^{\circ} \qquad \\ \\ \textbf{Rechnung:} \\ cos \alpha = \sqrt{1 - sin^{2} \alpha } \\ \alpha=45^{\circ}\\ cos 45^{\circ} = \sqrt{1 - sin^{2} 45^{\circ} }\\\\cos 45^{\circ}=0,707 \\\\\\ \small \begin{array}{|l|} \hline alpha=\\ \hline 45 ° \\ \hline 2,7\cdot 10^{3} \text{'} \\ \hline 1,62\cdot 10^{5} \text{''} \\ \hline 50 gon \\ \hline 0,785 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline cosalpha=\\ \hline 0,707 rad \\ \hline 707 mrad \\ \hline 40,5 ^\circ \\ \hline 2,43\cdot 10^{3} \text{'} \\ \hline 1,46\cdot 10^{5} \text{'''} \\ \hline \end{array} \end{array}$