Higher Trigonometry: A Class Of Nonlinear Systems

We study the initial value problem ‘$s,’ = c^{p - 1}, ; c,’ = -s^{p - 1}; ; ; s(0) = 0, ; c(0) = 1$’ (both as a real system and as a complex system) for each integer $p>2$, considering separately the cases ‘$p$ even’ and ‘$p$ odd’.