Polar Coordinates

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## Polar Coordinates

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**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.