Beatty Sequences and Trigonometric Functions

Beatty sequences are used to solve certain inequalities involving the tangent and sine functions. Fraenkel's theorem on nonhomogeneous Beatty sets is then used to determine integers for which certain products of sines are positive (or negative). Pairs of complementary nonhomogeous Beatty sets are recast as two pairs of complementary nonhomogeneous Beatty sequences. The final section poses a general question regarding the underlying connections between a broad class of functions and Beatty sequences.