Beside the Cartesian , there are other systems also for representing points and curve analytically . Polar system which is one of them .
---------In this system we started with a fixed line OX called the Initial Line and a fixed point on it , called the Pole .
---------If P be any given point, the distance OP=r is called the Radius Vector and Angle XOP=theta the Vectorial Angle . The two together are referred to as the Polar Co-ordinates of P .
Unrestricted Variation of Polar Co-ordinates :-
If we concerned with assigning polar co-ordinates to only individual points in the plane , then it would clearly be enough to consider the radius vector to have positive values only and the vectorial angle theta to lie between 0 and 2pi .
Transformation of Co-ordinates :-
Take the initial line OX of the polar system as the positive direction of X-axis and the Pole O as origin for the Cartesian system .The positive direction of Y-axis is to be such that the line OX after revolving through Half Pi is counter - clockwise direction comes to consider with it .
Polar Equation of Curves :-
Any explicit and implicit relation between r and theta will give a curve determined by the points whose co-ordinates satisfy that relation .
--------- Thus the Equations .
r=f(theta) or F(r,theta)
determines Curves .