A sinusoid or sine wave is a periodic wave whose shape is the trigonometric sine function.

Sine wave is heavily related to circular motions:

A sinusoid has the following form:

where

  • is the amplitude
  • is the independent variable (often representing time in seconds)
  • is the frequency, measured in hertz (Hz), representing the number of oscillations per second
  • is the angular frequency, in units of radians per second
  • is the phase (in radians), specifying the starting point of the oscillation at 1

Properties

  • Euler’s formula - Transform between the polar form of a complex number into sinusoids
  • Fourier series - Decompose functions into linear combination of sinusoids

Footnotes

  1. Sine wave - Wikipedia