Benutzer:Frankee 67/Formel

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

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