10.3 Polar Coordinates Cartesian coordinates: a point in the plane is represented by the distances from two perpendicular axes. y o x
Polar coordinates system:O - pole (or origin)Polar axis: a (horizontal) ray starting at OAny point P is represented by ( , ) . P r O Polar axis
Conventions: Pole is represented by ( , ) for any . is measured in the counter-clockwise direction. ( , ) represents the same point as ( , ). (− , ) represents the same point as (, + ).In polar coordinate system each point hasmany representations.
Connection between polar and Cartesiancoordinates system: = , = = + , =Converting polar coordinates to Cartesiancoordinates is easy, while representing thepoint with Cartesian coordinates in terms ofpolar coordinates is harder.
= , = = + , =Ex: Convert ( , / ) from polar to Cartesiancoordinates, convert ( , ) from Cartesianto polar coordinates.
Polar curves. Like in the Cartesian system, one polar equation represents a curve in general. Sometimes it is much simpler than the corresponding representation in the Cartesian system.Ex: What is the curve described by = ?What is the curve described by = ?