Trigonometric Graphs & the Unit Circle
Discover how the uniform rotation of a point on the unit circle maps perfectly into a continuous wave functions like Sine and Cosine.
About this simulation
- What
- An interactive Math simulation of Trigonometric Graphs & the Unit Circle.
- Who
- Designed for AP, IB, and A‑Level Math students.
- How
- Runs in any modern browser — drag, adjust, and explore in real time.
Updated 2026-04-03
Key Concepts
Amplitude (A)
The maximum absolute value from the horizontal axis. It visually stretches or compresses the wave vertically.
Frequency (ω)
Determines how fast the point rotates. Higher ω means tighter, higher-frequency waves.
Phase Shift (φ)
Shifts the starting position of the wave horizontally, acting as a mathematical 'head start' for the rotation.
The Origin of the Wave
Many students learn sine and cosine waves as abstract squiggly lines on a graph. However, they describe a very simple physical reality: a point spinning in a circle.
By tracking the horizontal (Cosine) or vertical (Sine) progress of that spinning point over time, the wave is painted naturally.