Standard
\(\csc (\theta ):=\dfrac{1}{\sin (\theta )}\)
\(\sec (\theta ):=\dfrac{1}{\cos (\theta )}\)
\(\cot (\theta ):=\dfrac{1}{\tan (\theta )}\)
Hyperbolic
\(csch (\theta ):=\dfrac{1}{\sinh (\theta )}\)
\(sech (\theta ):=\dfrac{1}{\cosh (\theta )}\)
\(coth (\theta ):=\dfrac{1}{\tanh (\theta )}\)
Reciprocal standard
\(\csc (arccsc (\theta )):=\theta\)
\(\sec (arcsec (\theta )):=\theta\)
\(\cot (arccot (\theta )):=\theta\)
Reciprocal hyperbolic
\(csch (arccsch (\theta )):=\theta\)
\(sech (arcsech (\theta )):=\theta\)
\(coth (arccoth (\theta )):=\theta\)
\(\sinh(\theta ):=\sin(i\theta )\)
\(\cosh(\theta ):=\cos(i\theta )\)
\(\tanh(\theta ):=\tan(i\theta )\)
\(\sinh (arcsinh (\theta )):=\theta\)
\(\cosh (arccosh (\theta )):=\theta\)
\(\tanh (arctan (\theta )):=\theta\)