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: 05
$ \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=120^{\circ} \qquad \\ \\ \textbf{Rechnung:} \\ cos \alpha = \sqrt{1 - sin^{2} \alpha } \\ \alpha=120^{\circ}\\ cos \alpha = \sqrt{1 - sin^{2} 120^{\circ} }\\\\cos \alpha=\frac{1}{2} \\\\\\ \small \begin{array}{|l|} \hline alpha=\\ \hline 120 ° \\ \hline 7,2\cdot 10^{3} \text{'} \\ \hline 4,32\cdot 10^{5} \text{''} \\ \hline 133\frac{1}{3} gon \\ \hline 2,09 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline cosalpha=\\ \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}$