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: 02
$\begin{array}{l} \text{Gegeben:}\\\text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \\ \text{Gesucht:} \\\text{Tangens alpha} \qquad tan \alpha \qquad [] \\ \\ tan \alpha = \frac{sin \alpha }{cos \alpha }\\ \textbf{Gegeben:} \\ \alpha=20^{\circ} \qquad \\ \\ \textbf{Rechnung:} \\ tan \alpha = \frac{sin \alpha }{cos \alpha } \\ \alpha=20^{\circ}\\ tan 20^{\circ} = \frac{sin 20^{\circ} }{cos 20^{\circ} }\\ \\ tan 20^{\circ}=0,364 \\\\\\ \small \begin{array}{|l|} \hline alpha=\\ \hline 20 ° \\ \hline 1,2\cdot 10^{3} \text{'} \\ \hline 7,2\cdot 10^{4} \text{''} \\ \hline 22\frac{2}{9} gon \\ \hline 0,349 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline Tanalpha=\\ \hline 0,364 rad \\ \hline 364 mrad \\ \hline 20,9 ^\circ \\ \hline 1,25\cdot 10^{3} \text{'} \\ \hline 7,51\cdot 10^{4} \text{'''} \\ \hline \end{array} \end{array}$