Parametric Equation/Examples/Circle

Examples of Parametric Equations

Let $\CC$ be the circle embedded in a Cartesian plane with the equation:

$x^2 + y^2 = 16$

This can be expressed in parametric equations as:

\(\ds x\)

\(=\)

\(\ds 4 \cos \theta\)

\(\ds y\)

\(=\)

\(\ds 4 \sin \theta\)

where $\theta$ is the parameter representing the angle between the $x$-axis and the point $\paren {x, y}$ on $\CC$.

Each point on $\CC$ corresponds exactly to a value of $\theta$ such that $\theta \in \hointr 0 {2 \pi}$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): parametric equations
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): parametric equations