Parametric equations: x = f(t), y = g(t). Circle: (cos t, sin t). Ellipse: (a cos t, b sin t). Lissajous: (sin(at), sin(bt+δ)). Cycloid: (t−sin t, 1−cos t). Derivatives: dy/dx = (dy/dt)/(dx/dt). Arc length: ∫√(x'²+y'²)dt.
How to Use
Select a curve:
- (x(t), y(t)): Parametric pair
- t range: Parameter interval
- Output: Point table
Famous Curves
- Lissajous: (sin(at), sin(bt))
- Cycloid: (t−sin t, 1−cos t)
- Cardioid: ((1+cosθ)cosθ, (1+cosθ)sinθ)
- Astroid: (cos³t, sin³t)
Calculus
Slope: dy/dx = y'(t)/x'(t). Arc length: L = ∫√(x'²+y'²)dt. Area: A = ∫y(t)x'(t)dt. Curvature: κ = |x'y''−y'x''|/(x'²+y'²)^(3/2).
Step-by-Step Instructions
- 1Select curve type.
- 2Set t range.
- 3View point table.
- 4Analyze coordinates.
- 5Check derivatives.