POLAR COORDINATES: WHAT THEY ARE AND HOW TO USE THEM MAHNOUD M.ALAMRE

الملخص

1- 1) Coordinate system:
Coordinate systems are really nothing more than a way to
define a point in space. For instance in the Cartesian
coordinate system at point is given the coordinates (x,y)
and we use this to define the point by starting at the origin
and then moving x units horizontally followed by y units
vertically. .This is not, however, the only way to define a
point in two dimensional space. Instead of moving
vertically and horizontally from the origin to get to the point
we could instead go straight out of the origin until we hit
the point and then determine the angle this line makes with
the positive x-axis. We could then use the distance of the
point from the origin and the amount we needed to rotate
from the positive x-axis as the coordinates of the point.
Coordinates in this form are called polar coordinates.
The usual Cartesian coordinate system can be quite
difficult to use in certain situations. Some of the most
POLAR COORDINATES: WHAT THEY ARE AND HOW TO USE
THEM MAHNOUD M.ALAMRE
common situations when Cartesian coordinates are difficult
to employ involve those in which circular, cylindrical,
Double Integrals or spherical symmetry is present. For
these situations it is often more convenient to use a
different coordinate system as Polar Coordinates.
The coordinate system as a rule. The most basic question
is: What is a coordinate system? The answer is so
important that I am going to state it in bold font: