The concept of phase can be readily understood in terms of simple harmonic motion. The same concept applies to wave motion, viewed either at a point in space over an interval of time or across an interval of space at a moment in time. Simple harmonic motion is a displacement that varies cyclically, as depicted below:
where A is the amplitude of oscillation, and f is the frequency. A motion with frequency f has period
is the elapsed time, and θ is the phase of the oscillation. It determines or is determined by the initial displacement at time t = 0.
The term instantaneous phase is used to distinguish the time-variant angle from the initial condition. It also has a formal definition that is applicable to more general functions and unambiguously defines a function's initial phase at t=0. I.e., sine and cosine inherently have different initial phases.