What is even and odd wave function?

A basic wave function is a sine or cosine function whose amplitude may have a value other than 1.

The cosine function is an even function because it is symmetrical about the y-axis. That is, f(-x) = f(x) for all x.

The sine function is an odd function because it is antisymmetrical about the y-axis. That is, f(-x) = -f(x) for all x.