Sine Wave
Classic Cartesian curvesThe graph y = A·sin(ωx) of pure oscillation — the atom every periodic signal is built from.
Adjust parameters
Equation
Open the Creator with a ready-made animation brief for this curve — review the scene plan and Manim code before rendering.
What is the Sine Wave?
The sine wave y = A·sin(ωx) is the shadow of uniform circular motion: project a point moving around a circle onto a line, stretch time along an axis, and this is the graph you get. Amplitude A sets the height, angular frequency ω sets how many radians fit per unit — the period is 2π/ω.
Its special status comes from Fourier’s theorem: any reasonable periodic signal decomposes into a sum of sines and cosines. That single fact makes the sine wave the working currency of acoustics, AC power, radio, and signal processing — and the first curve every trigonometry student learns to transform.
Key properties
- Period 2π/ω, amplitude A, zeros at x = kπ/ω.
- It is the projection of uniform circular motion onto a diameter.
- Derivative is a cosine — the same wave shifted left by a quarter period.
- Fourier’s theorem: periodic signals are sums of sines and cosines.
- Simple harmonic motion (mass on a spring, small pendulum) graphs as a sine wave in time.
Where you'll see it
Sound and radio waves, AC electricity, tides, oscilloscope screens, and every trigonometry classroom.