The argument of a trigonometric function (usually called angle) is a dimensionless quantity. Only in first expression, the angle. i.e., 2π/T x t is dimensionless. In other equations, the factor vt, (2π/t)t and (2π/v)t have dimensions of [L], [L-1 T2] respectively. Hence, the displacement of the particle is given only by the first expression, i.e.,[y = sin 2π/T x t].