Amplitude and period

Math

Definition

Amplitude is the distance from the midline to the maximum (or minimum) of a trigonometric function. Period is the horizontal length of one complete cycle. For y = A·sin(Bx), the amplitude is |A| and the period is 2π/|B|.

Examples

  • y = 3sin(2x) has amplitude 3 and period π
  • The height of a Ferris wheel over time can be modeled with amplitude equal to the wheel's radius and period equal to the time for one full rotation
Key Fact

Amplitude = |A|, Period = 2π/|B| for y = A·sin(Bx) or y = A·cos(Bx)

Related Terms

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

Study This Concept

Practice amplitude and period with free review games in these units:

Algebra 2 Unit 9: Trigonometric Functions