How to convert rectangular coordinates to polar coordinates, and vice-versa.
Rectangular coordinates and polar coordinates are two different ways of using two numbers to locate a point on a plane.
Rectangular coordinates are in the form (x,y), where 'x' and 'y' are the horizontal and vertical distances from the origin:
Polar coordinates are in the form: (r,q), where 'r' is the distance from the origin to the point, and 'q' is the angle measured from the positive 'x' axis to the point:
To convert between polar and rectangular coordinates, we make a right triangle to the point (x,y), like this:
1. Polar to Rectangular
From the diagram above, these formulas convert polar coordinates to rectangular coordinates:
So the polar point: (r,q) can be converted to rectangular coordinates like this:
Example: A point has polar coordinates: (5, 30º). Convert to rectangular coordinates.
Solution:Â (x,y) = (5cos30º, 5sin30º) = (4.3301, 2.5)
2. Rectangular to Polar
Again, from the diagram above, these formulas convert rectangular coordinates to polar coordinates:
So the rectangular point: (x,y) can be converted to polar coordinates like this:
Example: A point has rectangular coordinates: (3, 4). Convert to polar coordinates.
Solution:Â r = square root of(3² + 4²)
= 5,Â Â q
= tan-1(4/3) = 53.13º
Maths Helper Plus can convert your coordinates from rectangular to polar or polar to rectangular, showing a helpful diagram and all of the working steps.
Step 2Â Display the parameters box and enter values
Press the F5 key to display the parameters box:
Click on the edit boxes of the parameters box to enter the coordinates to convert.
1. To enter rectangular coordinates and convert them to polar coordinates:
2. To enter polar coordinates and convert them to polar coordinates:
Step 3Â Adjust the scale of the diagram
If the graph diagram is too large to fit on the plotting area of the screen, briefly press the F10 key. This doubles the scale range in the 'x' and 'y' directions and makes the diagram smaller. Repeat if necessary.
To enlarge the diagram again,Â hold down 'Shift' while you press F10.