Posted by bill on Monday, March 22, 2010 at 10:08am.
It is a very simple concept to learn
Polar coordinates have the form (r,Ø)
where r is the length of a rotating arm, usually r is positive, and Ø is the angle it points to.
So draw a standard x-y intersecting axes
the normal point (0,)) is the centre of rotation, with the positive x-axis as the 0 direction.
Rotation is counterclockwise.
so a polar point of (4,π/6) would be a rotating arm of length 4 rotated through π/6 radians or 30 degrees.
Unlike rectangular coordinates, polar coordinate points are not uniquely defined.
e.g. (5, π/3) ends up in the same place as (5,-5π/3) or (5,7π/3).
My angles are all coterminal, that is they end up in the same direction.
to convert from one to the other, ....
1. polar to rectangular:
x = rcosØ
y = rsinØ
2. rectangular to polar
r = √(x^2 + y^2) , which is just using Pythagoras
Ø = arctan(y/x)