Interactive circular function graph transformation widget

Every sine wave is just coordinates

The parameters in y = a sin(n(x − h)) + k aren't abstract — they're literal instructions for moving and stretching the graph. Drag the slider to change the amplitude and watch the wave reshape in real time.

Wave Transform Amplitude: 1.0
Adjust amplitude from -3 to +3
y = 1.0 sin(x)
-3 -1.5 0 1.5 3
Amplitude |a|
1.0
Range
[-1, 1]
The equation y = a sin(n(x − h)) + k is a coordinate system for transformations. The amplitude a stretches vertically (height of the wave). The coefficient n compresses horizontally — period becomes 2π/n. The h value slides the entire graph left or right (phase shift), and k moves it up or down (vertical shift). The range is always [k − a, k + a]. Every parameter has a geometric meaning you can point to on the graph.
Know This
For y = a sin(n(x − h)) + k: amplitude is |a|, period is 2π/n, h shifts the graph horizontally (phase shift), k shifts it vertically.