Instead of the Cartesian
coordinates x and y, the position of a point P in the plane can also be
characterized by
- its distance from the origin (usually
designated with the letter r) and
- the direction in which it is "seen"
from the origin. This direction is defined as the angle, relative
to the x axis (measured counter-clockwise). It is designated by the
Greek letter f (phi), j
(other variant of phi) or q (theta) also often
being used.
These coordinates are called (planar)
polar coordinates. The position of a point is defined by a pair
(r, f) of numbers. r is
always ³ 0 and 0°
£ f < 360°. (Please
note: an angle of 360° is the same as 0°).
This is not entirely true of the origin: At the origin,
r = 0, but the angle f
is completely undetermined. All other points have unambiguously determined
values of r and f, and in turn each pair (r,
f) for which
r > 0 and 0° £
f< 360° specifies exactly one point.
Some geometric problems can be solved more easily if the
drawing plane is seen through polar coordinates. In technical drawings, for
example rounded-off corners of parts are preferentially specified in
polar coordinates. |
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