Students will approximate pi by setting up trigonometric ratios and calculating the areas of regular polygons inscribed within and circumscribed about a circle.
During the Activity
Have the students draw a 30-60-90 triangle in the first diagram, with the hypotenuse extending from the center of the circle to a vertex of the triangle. Define an angle theta as a central angle of the circle.
After the Activity
Question #8 leads into a great introduction of limits.