Amplitude period phase shift

Math

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

  • 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
  • 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)

Related Terms

Amplitude and period Graphing sine and cosine Sine and cosine graphs Graphing trig functions

Study This Concept

Practice amplitude period phase shift with free review games in these units:

Pre-Calculus Unit 4: Trigonometric Functions