  Here we introduce a way to construct generalized trigonometric functions
associated with any complex polynomials, and the well known trigonometric
functions can be seen to associate with polynomial $x^2-1$. We will show that
those generalized trigonometric functions have algebraic identities which
generalizes the well known $\sin^2(x)+\cos^2(x)=1$. One application of the
generalized trigonometric functions is evaluating infinite series of rational
functions.
