x_{1} is a generalized-trigonometric function with properties x_{2}.

Not limited to normal trig functions such as sine, cosine, and tangent. It also includes havversine and the like, reciprocal trig functions (cosecant, secant, cotangent), the hyperbolic trig function (sinh, cosh, tanh), the function that is halfway between sine and cosine, complex exponentiation, the corresponding reciprocals to any of the aforementioned or following functions, and the inverse functions of any of these functions (principle or otherwise; these are the arc-trig functions and logarithms), and many other analogous concepts. For the standard (planar) set, qualify this word with words meaning "real planar", "Euclidean", or perhaps just "circle"/"triangle"; they can be restricted further. Specify "hyperbolic" for the corresponding functions.