Rectangular coordinates

Definition

Rectangular coordinates are a pair of numerical values that determine the position of a point in a two-dimensional plane, typically represented as $(x, y)$. They are used to describe points based on their horizontal (x-axis) and vertical (y-axis) distances from the origin.

5 Must Know Facts For Your Next Test

1. Rectangular coordinates are essential for converting between Cartesian and polar coordinate systems.
2. The distance from the origin to a point $(x, y)$ can be found using the formula $r = \sqrt{x^2 + y^2}$.
3. The angle $\theta$ in polar coordinates is calculated using $\theta = \arctan\left(\frac{y}{x}\right)$ when converting from rectangular coordinates.
4. Rectangular coordinates are also known as Cartesian coordinates.
5. In trigonometry, rectangular coordinates help in visualizing complex numbers on the complex plane.

Review Questions

• How do you convert rectangular coordinates $(x, y)$ to polar coordinates?
• What formula would you use to find the distance from the origin to the point $(3, 4)$?
• Explain how you would find the angle $\theta$ if given rectangular coordinates.

Related terms

Polar Coordinates: A coordinate system where each point is determined by its distance from a reference point (origin) and an angle from a reference direction.

Cartesian Plane: A two-dimensional coordinate system defined by a pair of perpendicular axes: x-axis (horizontal) and y-axis (vertical).

\arctan: $\arctan$ is the inverse tangent function, used to find an angle whose tangent is a given number.