Polar Coordinates • Review • Cartesian (or rectangular) coordinates are convenient for • Measuring distance from a point to the x or y axes • Translations However, it is inconvenient for rotations and measuring distances from the origin to a given point. In some applications, we are more interested in the distance from the origin to a given point and also the direction of that given point relative to the x-axis, therefore we need to create a new type of coordinates for those applications. For example, the air traffic controllers in a busy airport need to know how far the planes are from the airport and from which directions they are coming in.
Conversion from Polar to Cartesian Conversion from Cartesian to Polar
Disadvantages of the Polar Coordinates 1. The coordinates of a given point is never unique because the radius can be positive or negative, and the angle θ can be bigger than 360 2. At the Pole, the angle θ is undefined.
Polar Curves In polar coordinates, it is usually more convenient to express the radius r as a function of the angle , i.e. r = f () • Example: • r = 5 will produce a circle of radius 5 centered at the origin. • r = will produce a spiral starting at the Pole.