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: 01
$\text{Gegeben:}\\\text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \\ \text{Gesucht:} \\\text{Sinus alpha} \qquad sin \alpha \qquad [] \\ \\ sin \alpha = \sqrt{1 - cos^{2} \alpha }\\ \textbf{Gegeben:} \\ \alpha=30^{\circ} \qquad \\ \\ \textbf{Rechnung:} \\ sin \alpha = \sqrt{1 - cos^{2} \alpha } \\ \alpha=30^{\circ}\\ sin 30^{\circ} = \sqrt{1 - cos^{2} 30^{\circ} }\\\\sin \alpha=\frac{1}{2} \\\\\\ \small \begin{array}{|l|} \hline alpha=\\ \hline 30 ° \\ \hline 1,8\cdot 10^{3} \text{'} \\ \hline 1,08\cdot 10^{5} \text{''} \\ \hline 33\frac{1}{3} gon \\ \hline 0,524 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline sinalpha=\\ \hline \frac{1}{2} rad \\ \hline 500 mrad \\ \hline 28,6 ^\circ \\ \hline 1,72\cdot 10^{3} \text{'} \\ \hline 1,03\cdot 10^{5} \text{'''} \\ \hline \end{array}$