Parametric Equations and Polar Coordinates

Until now, we have worked solely with a rectangular coordinate system, in which there are two perpendicular axes, and points are specified according to their coordinates, (x, y). In the following lessons, we'll not only learn a new way to specify points in the rectangular coordinate system, but we'll also learn an entirely new coordinate system. The rectangular coordinate system is good for some applications, but has its limits. Parametric equations allow for us to graph things in a new way in the rectangular coordinate system. In parametric equations, the variables x and y are both functions of a third variable. Parametric equations are most often used to show the passage of time in a graph. The polar coordinate system is an entirely new coordinate system which allows for certain functions to be graphed using simpler equations. Instead of x and y, the polar coordinate system uses r and θ to specify points. We'll learn about the new coordinate system, and how to convert between rectangular coordinates and polar coordinates.