反三角函數

反三角函數係三角函數嘅反函數。

一覽

名	常用符號	定義	定義域	值域
反正弦	${\displaystyle y=\arcsin x}$	${\displaystyle x=\sin y}$	${\displaystyle [-1,1]}$	${\displaystyle [-{\frac {\pi }{2}},{\frac {\pi }{2}}]}$
反餘弦	${\displaystyle y=\arccos x}$	${\displaystyle x=\cos y}$	${\displaystyle [-1,1]}$	${\displaystyle [0,\pi ]}$
反正切	${\displaystyle y=\arctan x}$	${\displaystyle x=\tan y}$	${\displaystyle \mathbb {R} }$	${\displaystyle (-{\frac {\pi }{2}},{\frac {\pi }{2}})}$
反餘切	${\displaystyle y=\operatorname {arccot} x}$	${\displaystyle x=\cot y}$	${\displaystyle \mathbb {R} }$	${\displaystyle (0,\pi )}$
反正割	${\displaystyle y=\operatorname {arcsec} x}$	${\displaystyle x=\sec y}$	${\displaystyle (-\infty ,-1]\cup [1,+\infty )}$	${\displaystyle [0,{\frac {\pi }{2}})\cup ({\frac {\pi }{2}},\pi ]}$
反餘割	${\displaystyle y=\operatorname {arccsc} x}$	${\displaystyle x=\csc y}$	${\displaystyle (-\infty ,-1]\cup [1,+\infty )}$	${\displaystyle [-{\frac {\pi }{2}},0)\cup (0,{\frac {\pi }{2}}]}$