# Higher Trigonometry: A Class Of Nonlinear Systems

## TL;DR

This paper investigates a class of nonlinear systems derived from higher trigonometric functions, analyzing their behavior for different integer exponents and separating cases based on parity.

## Contribution

It introduces a systematic study of nonlinear initial value problems related to higher trigonometric functions for various integer powers, highlighting differences between even and odd cases.

## Key findings

- Characterization of solutions for even p
- Behavior analysis for odd p
- Extension to complex systems

## Abstract

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'.