Polar Cordinates:

Polar coordinates are of the form (r,q) where r is the distance from the origin and q is the angle made by that point with the x-axis.

Figure below shows how a polar coordinate point is plotted.

Objectives:

We alter the polar coordinates to rectangular coordinates and from rectangular coordinates to polar coordinates.The basic functions in polar coordinates using a graphing calculator. After running through these equipment, the student must be able

* to convert from rectangular coordinate to polar coordinates
* to convert from polar coordinate to rectangular coordinates
* to identify some standard polar graphs
* to plot point in polar coordinates
* to table polar equations using a graphing calculator.

# Coordinate systems are really nothing new than a manner to define a point in space.

# The Cartesian coordinate system at point is given the coordinate (x,y) and we use this to define the point by starting at the origin and then moving x units horizontally follow by y units vertically.

Converting Rectangular coordinates to Polar Coordinates:

To convert rectangular to polar co-ordinate consider the following right angle:

Rectangular to Polar Coordinates

From the above figure we can see x=r cosq and y=r sinq.

Now to find r square x and y and add them

x2+y2 = (r cosq)2+ (r sinq)2

x2+y2 = r2 cos 2q + r2 sin2q

x2+y2 = r2(cos2q + sin2q)

we know cos2q + sin2q=1

So x2+y2 = r2.

=> r = √(x2+y2)

An now to find q divide y over x

(y/x) = (r sinq/ r cosq)

=> tan q = y/x

q= tan -1(y/x)

So conversion from rectangular coordinates to polar coordinates is as below

(x , y) -------> (√(x2+y2),tan -1(y/x)) which is nothing but (r,q)

This is the procedure followed to convert rectangular coordinates to polar coordinates.

Hope you like the above example of Polar Cordinates.Please leave your comments, if you have any doubts.