Rectangular equation

Definition

A rectangular equation is an equation that expresses a relationship between $x$ and $y$ coordinates in the Cartesian coordinate system. These equations are typically written in the form $y = f(x)$ or $g(x, y) = 0$.

5 Must Know Facts For Your Next Test

1. Rectangular equations can be converted to polar equations by using the relationships $x = r\cos(\theta)$ and $y = r\sin(\theta)$.
2. In parametric equations, you can eliminate the parameter to get a rectangular equation.
3. Converting between rectangular and polar forms often involves trigonometric identities.
4. Graphing rectangular equations requires plotting points on the Cartesian coordinate system.
5. $r^2 = x^2 + y^2$ is a key relationship used when converting from polar coordinates to rectangular form.

Review Questions

• How do you convert the polar equation $r = 2\cos(\theta)$ to its rectangular form?
• What is the rectangular form of the parametric equations $x = t + 1$ and $y = t^2 - 1$?
• Which trigonometric identities are essential for converting between polar and rectangular coordinates?

Related terms

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

Parametric Equations: Equations that express the coordinates of points as functions of a variable called a parameter.

$r=\sqrt{x^2+y^2}$: $r=\sqrt{x^2+y^2}$ represents the radial distance in polar coordinates derived from rectangular coordinates.