Background to the problem: Many years ago I saw a generalization of trig functions to $n\ge 3$ functions. For the case of $n=3$, the unit circle or hyperbola was replaced by the solution surface of $x^3+y^3+z^3-3xyz=1$. A set of three parametric solutions to the equation was given (which would replace the usual pair of circular or hyperbolic sine and cosine).
Do you recall such a paper or know the parametrization?