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August 27, 2016
Posted by **bill** on Monday, March 22, 2010 at 10:08am.

- trig -
**Reiny**, Monday, March 22, 2010 at 10:59amIt 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)