arcctg ( − x ) = π − arcctg x {\displaystyle \operatorname {arcctg} \,(-x)=\pi -\operatorname {arcctg} \,x} (функцияның графигы ( 0 ; π 2 ) . {\displaystyle \left(0;{\frac {\pi }{2}}\right).} нөктәһенә ҡарата үҙәк симметрик. arcctg x > 0 {\displaystyle \operatorname {arcctg} \,x>0} при любых x . {\displaystyle x.} arcctg x = { arcsin ⁡ 1 1 + x 2 , x ⩾ 0 π − arcsin ⁡ 1 1 + x 2 , x < 0 {\displaystyle \operatorname {arcctg} \,x=\left\{{\begin{matrix}\arcsin {\frac {1}{\sqrt {1+x^{2}}}},\qquad x\geqslant 0\\\pi -\arcsin {\frac {1}{\sqrt {1+x^{2}}}},\qquad x<0\end{matrix}}\right.} arcctg ⁡ x = π / 2 − arctg ⁡ x . {\displaystyle \operatorname {arcctg} x=\pi /2-\operatorname {arctg} x.}