IntroParametric
Parametric Circle
x = r·cos t, y = r·sin t
Overview
A circle can be described parametrically using cosine and sine of an angle parameter t.
Domain
t ∈ [0, 2π]
Range
x ∈ [-r, r], y ∈ [-r, r]
Key Properties
1
t is the angle from the positive x-axis
2
r is the radius
3
Period: 2π (one full circle)
4
Center at origin; add (h, k) to translate
Key Insight
This is the basis for all circular motion — from Ferris wheels to planetary orbits.
Visualize Parametric Circle
Interact with the graph and explore this curve in the analytic geometry visualizer.