A sine wave is a smooth, periodic oscillation that is a fundamental waveform in mathematics and physics. It is defined by the function y = A sin(Bx + C) + D, where A represents the amplitude, B affects the frequency, C is the phase shift, and D is the vertical shift. Sine waves are commonly used to model various phenomena, such as sound waves and alternating current in electrical engineering. The shape of a sine wave resembles a continuous wave that rises and falls in a regular pattern. It is characterized by its smooth peaks and troughs, which occur at equal intervals. Sine waves are essential in fields like signal processing, music, and wave mechanics, as they represent the simplest form of oscillation.