Sine and cosine graphs

Math

Definition

The graphs of y = sin(x) and y = cos(x) are smooth, wave-shaped curves that repeat every 2π. The sine graph starts at the origin and the cosine graph starts at its maximum. Both have an amplitude of 1 and can be transformed by changing amplitude, period, phase shift, and vertical shift.

Examples

  • y = sin(x) crosses zero at 0, π, and 2π, and reaches its peak of 1 at π/2
  • y = 2cos(3x) has amplitude 2 and period 2π/3
  • Sound waves can be modeled using sine and cosine graphs
Key Fact

Period of y = sin(Bx) or y = cos(Bx) is 2π/|B|

Related Terms

Graphing sine and cosine Amplitude period and phase shift Graphing trig functions Unit circle

Study This Concept

Practice sine and cosine graphs with free review games in these units:

Trigonometry Unit 4: Graphing Trig Functions