Subject: How do you calculate displacement in the y-axis wrt x-axis in wave motion?

How do you calculate the displacement of a particle in the y-axis with respect to the displacement of the pulse in x-axis in a simple harmonic progressive wave? A formula says the following:
y[equ]a sin (wt+d)

where y[equ]displacement in y-axis
           x[equ] displacement in x-axis
           w[equ]angular velocity
            t[equ]time period (?)
           d[equ]delta (?)
Could you specify what t and d are. Also how does angular velocity come into the picture in a wave in which neither the particles nor the motion is in a non-rectilinear path?

Re: How do you calculate displacement in the y-axis wrt x-axis in wave motion?