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Wave Generator

Manipulate parameters to observe real-time transformations.

AA(Amplitude)
1.00

Adjusts vertical stretch (wave height).

ω\omega(Angular Frequency)
1.00

Adjusts horizontal stretch (number of waves).

ϕ\phi(Phase)
0.00

Adjusts horizontal shift (starting position).

06π

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.

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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.

Frequently Asked Questions