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.

Open Visualizer