The Cartesian Coordinate System describes space of one, two, and three dimensions. Each point in space is represented by its distance relative to the origin of the system. A point in two dimensional space (visualized below) is denoted as P = (x,y) where x represents the distance from the origin in the x-direction and y represents the distance from the origin in the y-direction. The point where the two axis meet is the origin and is represented by the point (0,0).

A point in one dimension only has one component: its distance from zero. This is visualized below.

In two dimensions the cartesian coordinate system describes where on a plane a point lies by using two components.

In three dimensional space a point has three components a x-component, y-component, and z-comonent: P = (x,y,z). For example, the coordinates of the point below is (3, 2, 3).

A common usage of the cartesian coordinate system is to visualize the input and output of a function. For example, the graph of the cosine function can be visualized in the 2D Cartesian Coordinate System below.

A function takes input and produces output. The idea is a useful way to abstract away complexity and, especially in the age of computers, is a practical tool to solve problems.

A collection of mathematical graphs. Each graph is scaled to demonstrate the properties of the function being graphed. Hover over the graph to dynamically see input and output. Use the mouse wheel or pinch to zoom in and out on the graph.

The cosine function returns the cosine of an angle provided in radians. In geometric terms, the function returns the ratio of the right-triangle's adjacent side over its hypotenuse.