Amplitude period and phase shift

Math

Definition

The three key transformations of a trigonometric function y = A·sin(B(x − C)) + D. Amplitude |A| controls vertical stretch, period 2π/|B| controls horizontal compression, phase shift C moves the graph left or right, and D shifts the midline vertically.

Examples

  • y = 2sin(3(x − π/4)) + 1 has amplitude 2, period 2π/3, phase shift π/4 right, and vertical shift up 1
  • Modeling seasonal temperature with amplitude for the temperature range, period of 12 months, and phase shift to align the peak with the hottest month
Key Fact

y = A·sin(B(x − C)) + D: amplitude |A|, period 2π/|B|, phase shift C, vertical shift D

Related Terms

Amplitude and period Graphing sine and cosine Graphing trig functions Transformations

Study This Concept

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

Trigonometry Unit 4: Graphing Trig Functions