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.

Joseph Lo, 27 March 2013, Created with GeoGebra