arccos ⁡ ( − x ) = π − arccos ⁡ x {\displaystyle \arccos(-x)=\pi -\arccos x} (функцияның графигы ( 0 ; π 2 ) {\displaystyle \left(0;{\frac {\pi }{2}}\right)} нөктәһенә ҡарата үҙәк симметрик), индифферентлы булып тора. arccos ⁡ x > 0 {\displaystyle \arccos x>0} при − 1 ⩽ x < 1. {\displaystyle -1\leqslant x<1.} arccos ⁡ x = 0 {\displaystyle \arccos x=0} при x = 1. {\displaystyle x=1.} arccos ⁡ x = π 2 − arcsin ⁡ x . {\displaystyle \arccos x={\frac {\pi }{2}}-\arcsin x.} arccos ⁡ x = { arcsin ⁡ 1 − x 2 , 0 ⩽ x ⩽ 1 π − arcsin ⁡ 1 − x 2 , − 1 ⩽ x < 0 {\displaystyle \arccos x=\left\{{\begin{matrix}\arcsin {\sqrt {1-x^{2}}},\qquad 0\leqslant x\leqslant 1\\\pi -\arcsin {\sqrt {1-x^{2}}},\qquad -1\leqslant x<0\end{matrix}}\right.} arccos ⁡ x = { arctg 1 − x 2 x , 0 < x ⩽ 1 π + arctg 1 − x 2 x , − 1 ⩽ x < 0 {\displaystyle \arccos x=\left\{{\begin{matrix}\operatorname {arctg} \,{\frac {\sqrt {1-x^{2}}}{x}},\qquad 0<x\leqslant 1\\\pi +\operatorname {arctg} \,{\frac {\sqrt {1-x^{2}}}{x}},\qquad -1\leqslant x<0\end{matrix}}\right.} arccos ⁡ x = 2 arcsin ⁡ 1 − x 2 {\displaystyle \arccos x=2\arcsin {\sqrt {\frac {1-x}{2}}}} arccos ⁡ x = 2 arccos ⁡ 1 + x 2 {\displaystyle \arccos x=2\arccos {\sqrt {\frac {1+x}{2}}}} arccos ⁡ x = 2 arctg ⁡ 1 − x 1 + x {\displaystyle \arccos x=2\operatorname {arctg} {\sqrt {\frac {1-x}{1+x}}}}