A cardioid is a heart-shaped curve described by the polar equation $r = a(1 + \cos\theta)$ or $r = a(1 + \sin\theta)$. It is a special type of limaçon and is symmetric about the x-axis or y-axis depending on its form.
5 Must Know Facts For Your Next Test
A cardioid can be generated by tracing a point on the circumference of a circle as it rolls around another circle of the same radius.
The Cartesian coordinates for points on the cardioid given by $r = a(1 + \cos\theta)$ are $(a(2\cos^2\frac{\theta}{2}), a(2\cos^2\frac{\theta}{2}) - 2a)$.
The area enclosed by the cardioid $r = a(1 + \cos\theta)$ is $3\pi a^2/2$.
The length of the arc of one loop of the cardioid $r = a(1 + \cos\theta)$ is $8a$.
Cardioids exhibit cusp singularities at their vertices, where the derivative with respect to $\theta$ becomes undefined.