## Polar Function

To draw a curve $$r = r(\theta)$$ in polar coordinates, we can first plot $$r(\theta)$$ on the $$\theta r$$-plane as a normal function. Consider the function $r(\theta) = 2\sin (3\theta).$ On the $$\theta r$$-plane, this function is a sinusoidal curve with amplitude 2 and period $$2\pi/3$$. The curve is shown in the left graph with the length of the green arrow indicating the value of $$r(\theta)$$.

The right graph shows the polar curve. As you move the slider (to change the value of $$\theta$$), the length of the green arrow in the right graph is exactly the value $$r(\theta)$$. With this information, you can determine how the polar curve look like.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Joseph Lo, 27 March 2013, Created with GeoGebra