Math

Amplitude period phase shift.

Definition

The three key parameters that describe a sinusoidal function. Amplitude measures the height from the midline, period measures the length of one complete cycle, and phase shift indicates the horizontal displacement from the standard position.

Examples

Real-world.

  • 1 For y = 4cos(2x − π), rewrite as y = 4cos(2(x − π/2)) to see amplitude 4, period π, and phase shift π/2 right
  • 2 A sound wave with larger amplitude is louder, shorter period means higher pitch, and phase shift represents a time delay
Key Fact

Amplitude = |A|, Period = 2π/|B|, Phase shift = C (from y = A·sin(B(x − C)) + D)

Studied in

1 unit use this concept.