1)\(\displaystyle{ arcsinx=-arcsin(-x)=\frac{\pi}{2}-arccosx}\) dla \(\displaystyle{ x{\in}[-1;1]}\)
2)\(\displaystyle{ arccosx=\pi-arccos(-x)=\frac{\pi}{2}-arcsinx}\) dla \(\displaystyle{ x{\in}[-1;1]}\)
3)\(\displaystyle{ arctgx=-arctg(-x)=\frac{\pi}{2}-arcctgx}\) dla \(\displaystyle{ x{\in}R}\)
4)\(\displaystyle{ arctgx+arctgy=arctg\frac{x+y}{1-xy}}\) dla \(\displaystyle{ xy y{\in}R xy{\neq}1}\)
5)\(\displaystyle{ arccosx=arcsin\sqrt{1-x^{2}}=arcctg\frac{x}{\sqrt{1-x^{2}}}}\) dla \(\displaystyle{ x{\in}[0;1]}\)
6)\(\displaystyle{ arctgx=arccos\frac{1}{\sqrt{1+x^{2}}}=arcctg\frac{1}{x}}\) dla \(\displaystyle{ x{\neq}0}\)
7)\(\displaystyle{ arcsin=arccos\sqrt{1-x^{2}}=arctg\frac{x}{\sqrt{1-x^{2}}}}\) dla \(\displaystyle{ x{\in}[0;1]}\)
8)\(\displaystyle{ sin (arc sin x + arc cos x) = sin (arc sin x) {\cdot}cos (arc cos x) + sin (arccos x){\cdot}cos (arc sin x)}\)