I'm looking to describe the feasible set of $x_1, \ldots, x_n$ for the following inequality:
$$a_1\cos x_1 + a_2\cos x_2 + \cdots+ a_n\cos x_n \ge 0$$
For variables $x_1, \ldots, x_n$ restricted to domain $-k\pi \le x_i \le k\pi$ , $k \ge 1$ an integer, and $a_i$ are real numbers.
Is this even possible to describe analytically?
EDIT - I should mention that numerical methods would be very welcome as well. For example, if the problem could somehow be split up into finding $x$ satisfying the intersection of a bunch of convex sets that would be fantastic.