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{Kosinus alpha} \qquad cos \alpha \qquad [] \\ \\ cos \alpha = \frac{sin \alpha }{tan \alpha }\\ \textbf{Gegeben:} \\ \alpha=15^{\circ} \qquad \\ \\ \textbf{Rechnung:} \\ cos \alpha = \frac{sin \alpha }{tan \alpha } \\ \alpha=15^{\circ}\\ cos \alpha = \frac{sin 15^{\circ} }{tan 15^{\circ} }\\\\cos \alpha=0,966 \\\\\\ \small \begin{array}{|l|} \hline alpha=\\ \hline 15 ° \\ \hline 900 \text{'} \\ \hline 5,4\cdot 10^{4} \text{''} \\ \hline 16\frac{2}{3} gon \\ \hline 0,262 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline cosalpha=\\ \hline 0,966 rad \\ \hline 966 mrad \\ \hline 55,3 ^\circ \\ \hline 3,32\cdot 10^{3} \text{'} \\ \hline 1,99\cdot 10^{5} \text{'''} \\ \hline \end{array}$