Notes (see the **Notes page** for further details of the various Notes collections).

Polar coordinates are simply a way of defining the position of a point in 2 dimensions. The distance from the origin (r) and the angle made with the x axis (measure in an anti-clockwise direction) define the position of the point. The point in the above diagram is a distance 3 from the origin and the angle made with the x axis is 30°.

Try this page on **Desmos to experiment with plotting points. **

Try a **join the dots exercise**! Polar Curves Join the dots

For some excellent resources on polar curves see **these** from the **mathcentre **and for some polar graph paper, **scroll down the page on Mathsbits.**

You can very easily experiment with families of polar curves using the excellent Desmos graphing calculator. Click on the image below and experiment with the sliders.

- Desmos polar curve, click on the image to experiment

It is possible to see how polar curves are traced out by using a slider in the domain on the Desmos graphing calculator. Try selecting the image to see r=acoskθ.

Further examples: **r=acos**^{2}θ, **r=a(1-cosθ) ****r=ae**^{-kθ} r^{2}=a^{2}cos2**θ**

Cardioids** a+bsinθ** and **a + bcosθ**

When do you get a dimple?

When do you get an inner loop?

Alternatively, try this **Polar Grapher**; use the slider to change the angle and you will see how the curve is traced out. Note the value of R is displayed so you can easily see if it is positive or negative.

For a really clear plotter showing the connection between the Cartesian graph of r=f(θ) and the graph in polar coordinates try this **Polar Curves and Cartesian Graphs applet**. Watch the display carefully as you move the slider; you can easily see when r is negative for example.

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