\[sinx = \frac{a}{c}\]

\[cosx = \frac{b}{c}\]

\[tgx = \frac{a}{b}\] (probabyl)

\[sin^2x = 1 - cos^2x\]

\[tgx = \frac{sinx}{cosx}\]

That are the most important "axioms" for me though. They helped me to get equation for coordinates of a sphere cut.