Benutzer:Frankee 67/Formel

Vielecke

Dreieck

Gleichseitiges Dreieck

Höhe

$a^{2}=\left({\frac {a}{2}}\right)^{2}+h^{2}\,\Rightarrow \,h={\frac {a}{2}}{\sqrt {3}}$

Wichtige Funktionswerte

α °	α (rad)	sin α	cos α	tan α	cot α
$0^{\circ }$	$\,0$	$\,0$	$\,1$	$\,0$	$\pm \infty$
$15^{\circ }$	${\tfrac {\pi }{12}}$	${\tfrac {1}{4}}({\sqrt {6}}-{\sqrt {2}})$	${\tfrac {1}{4}}({\sqrt {6}}+{\sqrt {2}})$	$2-{\sqrt {3}}$	$2+{\sqrt {3}}$
$18^{\circ }$	${\tfrac {\pi }{10}}$	${\tfrac {1}{4}}\left({\sqrt {5}}-1\right)$	${\tfrac {1}{4}}{\sqrt {10+2{\sqrt {5}}}}$	${\tfrac {1}{5}}{\sqrt {25-10{\sqrt {5}}}}$	${\sqrt {5+2{\sqrt {5}}}}$
$30^{\circ }$	${\tfrac {\pi }{6}}$	${\tfrac {1}{2}}$	${\tfrac {1}{2}}{\sqrt {3}}$	${\tfrac {1}{3}}{\sqrt {3}}$	${\sqrt {3}}$
$36^{\circ }$	${\tfrac {\pi }{5}}$	${\tfrac {1}{4}}{\sqrt {10-2{\sqrt {5}}}}$	${\tfrac {1}{4}}\left(1+{\sqrt {5}}\right)$	${\sqrt {5-2{\sqrt {5}}}}$	${\tfrac {1}{5}}{\sqrt {25+10{\sqrt {5}}}}$
$45^{\circ }$	${\tfrac {\pi }{4}}$	${\tfrac {1}{2}}{\sqrt {2}}$	${\tfrac {1}{2}}{\sqrt {2}}$	$1\,$	$1\,$
$54^{\circ }$	${\tfrac {3\pi }{10}}$	${\tfrac {1}{4}}\left(1+{\sqrt {5}}\right)$	${\tfrac {1}{4}}{\sqrt {10-2{\sqrt {5}}}}$	${\tfrac {1}{5}}{\sqrt {25+10{\sqrt {5}}}}$	${\sqrt {5-2{\sqrt {5}}}}$
$60^{\circ }$	${\tfrac {\pi }{3}}$	${\tfrac {1}{2}}{\sqrt {3}}$	${\tfrac {1}{2}}$	${\sqrt {3}}$	${\tfrac {1}{3}}{\sqrt {3}}$
$72^{\circ }$	${\tfrac {2\pi }{5}}$	${\tfrac {1}{4}}{\sqrt {10+2{\sqrt {5}}}}$	${\tfrac {1}{4}}\left({\sqrt {5}}-1\right)$	${\sqrt {5+2{\sqrt {5}}}}$	${\tfrac {1}{5}}{\sqrt {25-10{\sqrt {5}}}}$
$75^{\circ }$	${\tfrac {5\pi }{12}}$	${\tfrac {1}{4}}({\sqrt {6}}+{\sqrt {2}})$	${\tfrac {1}{4}}({\sqrt {6}}-{\sqrt {2}})$	$2+{\sqrt {3}}$	$2-{\sqrt {3}}$
$90^{\circ }$	${\tfrac {\pi }{2}}$	$\,1$	$\,0$	$\pm \infty$	$\,0$
$108^{\circ }$	${\tfrac {3\pi }{5}}$	${\tfrac {1}{4}}{\sqrt {10+2{\sqrt {5}}}}$	${\tfrac {1}{4}}\left(1-{\sqrt {5}}\right)$	$-{\sqrt {5+2{\sqrt {5}}}}$	$-{\tfrac {1}{5}}{\sqrt {25-10{\sqrt {5}}}}$
$120^{\circ }$	${\tfrac {2\pi }{3}}$	${\tfrac {1}{2}}{\sqrt {3}}$	$-{\tfrac {1}{2}}$	$-{\sqrt {3}}$	$-{\tfrac {1}{3}}{\sqrt {3}}$
$135^{\circ }$	${\tfrac {3\pi }{4}}$	${\tfrac {1}{2}}{\sqrt {2}}$	$-{\tfrac {1}{2}}{\sqrt {2}}$	$-1\,$	$-1\,$
$180^{\circ }$	$\pi \,$	$\,0$	$\,-1$	$\,0$	$\pm \infty$
$270^{\circ }$	${\tfrac {3\pi }{2}}$	$\,-1$	$\,0$	$\pm \infty$	$\,0$
$360^{\circ }$	$2\pi$	$\,0$	$\,1$	$\,0$	$\pm \infty$