The story The names even function and odd function come from the powers: $x^2$, $x^4$, $x^6$, … do not change when we change $x$ to $-x$, and $x$, $x^3$, $x^5$, … change signs. The terms appear in a work by the young Leonhard Euler on a curve problem proposed at the time, “reciprocal trajectories”, written around 1727. Euler also realized that the cosine behaves like even powers and the sine like odd powers, which is clear in the series he used: $\cos x = 1 - \frac{x^2}{2} + \frac{x^4}{24} - \cdots$ only has even powers, and $\operatorname{sen} x = x - \frac{x^3}{6} + \frac{x^5}{120} - \cdots$, only odd ones.