arcsin ⁡ ( − x ) = − arcsin ⁡ x {\displaystyle \arcsin(-x)=-\arcsin x\qquad } (таҡ функция). arcsin ⁡ x > 0 {\displaystyle \arcsin x>0} 0 < x ⩽ 1 {\displaystyle 0<x\leqslant 1} булғанда {\displaystyle \arcsin x>0} . arcsin ⁡ x = 0 {\displaystyle \arcsin x=0} x = 0. {\displaystyle x=0.} arcsin ⁡ x < 0 {\displaystyle \arcsin x<0} при − 1 ⩽ x < 0. {\displaystyle -1\leqslant x<0.} arcsin ⁡ x = { arccos ⁡ 1 − x 2 , 0 ⩽ x ⩽ 1 − arccos ⁡ 1 − x 2 , − 1 ⩽ x < 0 {\displaystyle \arcsin x=\left\{{\begin{matrix}\arccos {\sqrt {1-x^{2}}},\qquad 0\leqslant x\leqslant 1\\-\arccos {\sqrt {1-x^{2}}},\qquad -1\leqslant x<0\end{matrix}}\right.} arcsin ⁡ x = arctg ⁡ x 1 − x 2 {\displaystyle \arcsin x=\operatorname {arctg} {\frac {x}{\sqrt {1-x^{2}}}}} arcsin ⁡ x = { arcctg 1 − x 2 x , 0 < x ⩽ 1 arcctg 1 − x 2 x − π , − 1 ⩽ x < 0 {\displaystyle \arcsin x=\left\{{\begin{matrix}\operatorname {arcctg} \,{\frac {\sqrt {1-x^{2}}}{x}},\qquad 0<x\leqslant 1\\\operatorname {arcctg} \,{\frac {\sqrt {1-x^{2}}}{x}}-\pi ,\qquad -1\leqslant x<0\end{matrix}}\right.}