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Analytic Geometry2D

Polar Coordinates - Theory & Concepts - Analytic Geometry Polar Curves Rose Limacon

Polar coordinate system, conversion between rectangular and polar, and graphing polar curves.

Open the complete lesson

Polar Curves: Rose & Limaçon Explorer

Parameters

Parameter a (Base scale)5
Petal frequency integer n5

If $n$ is odd, the rose has $n$ petals. If $n$ is even, it has $2n$ petals.

Tracing Control

Angle Limit (θ_max)360°

Dynamic coordinate solver

Polar Equation
r=acos⁡(nθ)  ⟹  r=5.0cos⁡(5θ)r = a \cos(n \theta) \implies r = 5.0 \cos(5 \theta)
Step 1: Current Radius
θ=360∘ (6.283 rad)  ⟹  r=5.000\theta = 360^{\circ} \ ( 6.283 \text{ rad} ) \implies r = 5.000
Step 2: Polar to Cartesian conversion
x=rcos⁡(θ)=5.00cos⁡(360∘)=5.00y=rsin⁡(θ)=5.00sin⁡(360∘)=−0.00\begin{aligned} x &= r \cos(\theta) = 5.00 \cos(360^{\circ}) = 5.00 \\ y &= r \sin(\theta) = 5.00 \sin(360^{\circ}) = -0.00 \end{aligned}
Point P (r=5.00, θ=360°)

The dashed line shows the completed shape. The blue line traces the curve up to θ = 360°

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