Cartesian equation

Definition

A Cartesian equation is an algebraic equation that describes a curve in the Cartesian coordinate system. It typically involves variables x and y, representing coordinates on the plane.

5 Must Know Facts For Your Next Test

1. A Cartesian equation can be converted into a polar equation and vice versa.
2. Cartesian equations often take forms like lines ($y = mx + b$), circles ($x^2 + y^2 = r^2$), and ellipses ($\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$).
3. In the context of trigonometry, converting Cartesian equations to polar form involves substituting $x = r \cos(\theta)$ and $y = r \sin(\theta)$.
4. The process of converting between Cartesian and polar equations is essential for solving problems involving polar coordinates.
5. Understanding how to graph Cartesian equations helps in visualizing their corresponding polar forms.

Review Questions

• How do you convert the Cartesian equation $x^2 + y^2 = 25$ into its polar form?
• What are the steps involved in transforming $y = 3x + 4$ into a polar equation?
• Why is it useful to convert between Cartesian and polar equations?

Related terms

Polar Equation: An equation that represents a curve using the polar coordinate system, involving radius (r) and angle (θ).

Cartesian Coordinates: A coordinate system that specifies each point uniquely by a pair of numerical coordinates (x, y).

Conic Sections: Curves obtained by intersecting a plane with a double-napped cone; includes ellipses, parabolas, and hyperbolas.