Parametric equations

Definition

Parametric equations represent a set of related quantities as explicit functions of one or more independent variables called parameters. They are often used to describe the motion of objects and to graph complex curves.

5 Must Know Facts For Your Next Test

1. Parametric equations involve two or more equations with a common parameter, typically denoted as $t$.
2. The parametric form of a curve in the plane is given by $x(t) = f(t)$ and $y(t) = g(t)$ for a parameter $t$ within an interval.
3. Eliminating the parameter $t$ can sometimes convert parametric equations into a single Cartesian equation.
4. Parametric equations are particularly useful for modeling periodic phenomena and motions that cannot be described using simple Cartesian forms.
5. Graphing parametric equations involves plotting points $(x(t), y(t))$ for various values of $t$ and connecting these points smoothly.

Review Questions

• What is the role of the parameter in parametric equations?
• How would you graph the parametric equations $x(t) = \cos(t)$ and $y(t) = \sin(t)$?
• Explain how you can eliminate the parameter to find a Cartesian equation from given parametric equations.

Related terms

Cartesian Equation: An equation that relates x and y coordinates directly without involving any parameters.

Parameter: An independent variable used in parametric equations to express other variables as functions.

Polar Coordinates: A coordinate system where each point on a plane is determined by an angle and a distance from a reference point.