I want to define a function that would symbolically look like
$$ t(s,\underline{a})=\pi s + \sum_{n=1}^{n_{max}}a_n\sin(n \pi s) $$
(something like a finite Fourier series). Here $s\in [0,1]$ and $\underline a$ is a vector with $n_{max}$ entries $a=(a_1,...,a_i,...,a_{n_{max}})$.
Is there a short way to define such a function without having to name all the single $a_i$ in the function definition but take a vector as the input variable? My try was to define it just straightforward like
t[s_?NumericQ, a1_?NumericQ, a2_?NumericQ, a3_?NumericQ, a4_?NumericQ,
a5_?NumericQ, ...] := ...
but that gets really confusing for higher $n_{max}$.
So many thanks for any trick to handle it better :)