Wednesday, 1 January 2014

Polar Co-ordinates


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     .

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 .

No comments:

Post a Comment

Our Latest Post

How to find log (alpha+ i beta), Where alpha and beta are real

Here is the video to show the details of solving this problem. It is an important problem for basic understanding about the logarithm of re...

Popular Post