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{Tangens alpha} \qquad tan \alpha \qquad [] \\ \\ tan \alpha = \frac{sin \alpha }{cos \alpha }\\ \textbf{Gegeben:} \\ \alpha=5^{\circ} \qquad \\ \\ \textbf{Rechnung:} \\ tan \alpha = \frac{sin \alpha }{cos \alpha } \\ \alpha=5^{\circ}\\ tan 5^{\circ} = \frac{sin 5^{\circ} }{cos 5^{\circ} }\\ \\ tan 5^{\circ}=0,0875 \\\\\\ \small \begin{array}{|l|} \hline alpha=\\ \hline 5 ° \\ \hline 300 \text{'} \\ \hline 1,8\cdot 10^{4} \text{''} \\ \hline 5\frac{5}{9} gon \\ \hline 0,0873 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline Tanalpha=\\ \hline 0,0875 rad \\ \hline 87,5 mrad \\ \hline 5,01 ^\circ \\ \hline 301 \text{'} \\ \hline 1,8\cdot 10^{4} \text{'''} \\ \hline \end{array}$