These instructions are based on the use of xfig (version 3.1 or later). Another drawing program could certainly be used instead, and, indeed, colored chalk on the blackboard does OK too.
Start with this xfig file showing the axes, the unit circle, and the circular sector. Load it into xfig, and set the line width to 6, pen color to gold, fill color to yellow, and depth to 7. Use the polygon drawing tool to draw the inscribed triangle, and so deduce the first inequality. Next change the line width to 8, fill color to red, pen color to red2, and depth to 1, and draw the circumscribed triangle, which leads to the second inequality.
Last modified May 8, 1995 by Douglas N. Arnold