Graphing sine and cosine

Math

Definition

The process of plotting the sine and cosine functions, which produce smooth wave-shaped curves that repeat every 2π (360°). Key features include amplitude, period, phase shift, and midline.

How It Works

  1. Identify the amplitude |a|, period 2π/|b|, phase shift −c/b, and vertical shift d from y = a·sin(bx + c) + d.
  2. Mark the midline at y = d.
  3. Plot key points: start, quarter period, half period, three-quarter period, and full period.
  4. Connect the points with a smooth wave curve.
  5. Extend the pattern in both directions as needed.

Examples

  • y = sin(x) oscillates between −1 and 1 with period 2π
  • y = 3cos(2x) has amplitude 3 and period π
  • Sound waves and tidal patterns follow sinusoidal graphs
Key Fact

y = a·sin(b(x − h)) + k: amplitude = |a|, period = 2π/|b|, phase shift = h, midline = k

Related Terms

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

Study This Concept

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

Algebra 2 Unit 9: Trigonometric Functions