# Cardioid polar equation

## Cardioid (Definition, Equations and Examples)

To make a vertically oriented cardioid, the equation is: r = a ± a sin(θ) r = a ± a sin θ This equation gives you both a right-side up and upside-down cardioid: [insert drawing of both right-side-up and upside-down vertical cardioids] Cardioid

## What is a Cardioid?

How to: Given a polar equation, test for symmetry. Substitute the appropriate combination of components for (r, θ): ( − r, − θ) for θ = π 2 symmetry; (r, − θ) for polar axis symmetry; and ( − r, θ) for symmetry with respect to the pole. If the
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## Polar Equations

The polar equation of a cardioid is r = 2a(1 + cosθ), which looks like this with a=1: So, the area inside a cardioid can be found by A = ∫ 2π 0 ∫ 2a(1+cosθ) 0 rdrdθ = ∫ 2π 0 [ r2 2]2a(1+cosθ) 0 dθ = ∫ 2π 0 [2a(1 + cosθ)]2 2 dθ

## Graphing Basic Polar Equations

Polar Equation of Cardioid The polar equation of the horizontal cardioid is given by; r = a (1 ± cosθ) Similarly, the polar equation of the vertical cardioid is given

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## Equation of Cardioid/Polar

The cardioid has Cartesian equation (3) and the parametric equations (4) (5) The cardioid is a degenerate case of the limaçon. It is also a 1-cusped epicycloid (with ) and is the catacaustic formed by rays originating at a

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