Pattern with $\sec(x)$ partial sums

Question

I calculated with Wolfram|Alpha the partial sums of $S(x) = \sum^{x}_{n=0} \sec(n)$ and when I plot them I get a repeating pattern:

Which I thought would not happen given the fact that $\sec(x)$'s period is an irrational number ($\tau$). Any explanation for this wave's existance in this equation?