Coordinates are of two types; one is Cartesian coordinates and second is Polar Coordinates. We can convert polar coordinates to Cartesian coordinates and from Cartesian coordinates to polar coordinates.
Basically we use graph to mark these coordinates. Cartesian coordinates consist of two points, position on x- axis and Position of y- axis. These coordinates define how far an object is from origin. Polar coordinates also have coordinates as x and y- axis, which defines the position of the object on the graph but in addition it also has angles defined. This angle lies between x- axis and y- axis.
Four points are required to convert the coordinates from one form to another. These are position of x and y- axis, hypotenuse and angle which lie between the x and y- axis.
Let us see how we can convert polar coordinates to Cartesian coordinates: In polar coordinates we are given two points 'r' and angle 'θ'. Here side 'r' is √x2 + y2. When we convert polar coordinates to Cartesian coordinates we need to calculate ‘x’ and ‘y’ points.
In polar form the x- coordinates are associated with cos function and y- coordinates are associate with sin function.
Let us understand the conversion of polar to Cartesian with an example. Assume we have polar coordinates 'r' and 'θ' as (13, 22.60). Now we have to calculate x and y axes.
So cos(22.60) = x / 13 => x = 12.006
This is the position of x- axis on the graph.
Now calculate the y axis: sin (22.60) = y / 13 => 4.996,
This is the position of y- coordinates. Now Cartesian coordinates are (12, 5).