Polar Coordinates

Polar coordinates provide an alternate way of describing the location of a point P in the plane.

Relationship between polar coordinates and Cartesian coordinates   If a Cartesian (also called rectangular) coordinate system is already given, then there is a standard way of introducing, in addition, a polar coordinate system, namely:

• We place the pole at the origin.
• We choose the positive x-axis as the reference directional ray.

Now we have two coordinate systems superimposed on one another in the plane. We would like to be able to convert from one kind of coordinates into the other. Accordingly, we have

I.    Conversion of Polar Coordinates into Cartesian Coordinates

II.    Conversion of Cartesian Coordinates into Polar Coordinates

We present two methods of finding polar coordinates for a point P whose Cartesian coordinates (x,y) are known:

Exercises   on converting between Cartesian and polar coordinates.
1    2    3    4    5    6    7

Move on to

• the Polar coordinate transformation
• Cylindrical coordinates
• Spherical coordinates