Plotting polar coordinates
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How to plot polar coordinates on a graph.

This topic is part of the TCS FREE high school mathematics 'How-to Library'. It introduces the concept of polar coordinates, and shows you how to plot polar coordinates on a graph.
(See the index page for a list of all available topics in the library.) To make best use of this topic, you need to download the Maths Helper Plus software. Click here for instructions.


Polar coordinates locate a point on a plane with one distance and one angle. The distance ‘r’ is measured from the origin. The angle, ‘q' (Greek letter ‘theta’) is measured from some agreed starting point.

Use the positive part of the ‘x’ asix as the starting point for measuring angles. Measure positive angles anticlockwise from the positive ‘x’ axis, and negative angles clockwise from the positive 'x' axis.

 This diagram shows how the polar point ( 4, 50° ) is located:

Step 1: Measure the distance to a point 4 units from the origin along the positive ‘x’ axis.

Step 2: Rotate the point anticlockwise about the origin through angle 50°.


A. Learning about polar coordinates:

If you are still unsure about how to plot polar points on a graph grid, or you would like to try our fun polar coordinate plotter, we recommend this section (part A), otherwise you can proceed to part B.

Step 1 Download the free support file... We have created a Maths Helper Plus document containing the completed example from this topic. You can use this to practice the steps described below, and as a starting point for solving your own problems.

File name:  'Coordinate plotter (polar).mhp'   File size: 21kb
Click here to download the file.

If you choose 'Open this file from its current location', then Maths Helper Plus should open the document immediately. If not, try the other option: 'Save this file to disk', then run Maths Helper Plus and choose the 'Open' command from the 'File' menu. Locate the saved file and open it. If you do not yet have Maths Helper Plus installed on your computer, click here for instructions.


Step 2  Display the parameters box

Press the F5 key to display the parameters box:


Click on the 'A' edit box with the mouse, then type the 'r' value of your polar point. 

Similarly, click on the 'B' edit box and type the angle 'q' of your polar point in degrees. 

Click the 'Update' button to refresh the diagram.

B. Plotting polar coordinates:

This is how you can plot a set of polar coordinates in Maths Helper Plus, without using the polar plotter from part B above.

Step 1  Start with an empty Maths Helper Plus document

If you have just launched the software then you already have an empty document, otherwise hold down ‘Ctrl’ while you briefly press the ‘N’ key.


Step 2  Enter your [r,q] points

When plotting polar points in Maths Helper Plus, you use square brackets for each point, like this:

[4, 30ºor  [4, 30degor  [4, pi/6]

The angle is in radians by default, so if you want to enter degrees you have to type 'deg' after the angle, or use the degree symbol:  º . The third example: [4, pi/6] has the angle in radians, so no degree symbol is included.


NOTE: The degree symbol: º can be created by clicking on the popup 'shortcuts box' in Maths Helper Plus.


1. Press the F3 key to activate the 'input box' for typing (see below):

2. Type your own points into the input box, like this:


3. Press Enter to complete the entry


Step 3  Adjust the scale of the graph

If the graph scale is too small to display all of the points, briefly press the F10 key. This doubles the scale range in the 'x' and 'y' directions. Repeat until all plotted points are visible.


To reduce the scale again,  hold down 'Shift' while you press F10.


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