Since both x and y can be any real numbers, 3x + 4y can generate arguments for the cosine over all of [0,2π]. Hence, the output of the cosine function should cover the full range of [-1,1].
You know that
-1 ≤ cos(3x + 4y) ≤ 1
x = π/3 and y = 0 gives -1.
x = 0 and y = 0 gives 1.
You can see that you span the entire range of [-1,1].