Draw a (fairly large) circle on a blank sheet of paper. We’ll think of this as a unit circle.
Divide the unit circle into equal wedges each with its vertex at the center of the circle . On each wedge, call the
two corners of the wedge that lie on the circle and . Let denote the area of the triangle and let denote the
measure of the angle at . Explain how to estimate the area of the circle with triangle . What is your
estimate?
Divide the unit circle into equal wedges each with its vertex at the center of the circle . On each wedge, call the
two corners of the wedge that lie on the circle and . Let denote the area of the triangle and let denote the
measure of the angle at . Explain how to estimate the area of the circle with triangle . What information do you
need to know to actually do this computation?
Given an angle , explain the relation of and to the unit circle. How could these values help with the calculation
described above?
Divide the unit circle into equal wedges each with its vertex at the center of the circle . On each wedge, call
the two corners of the wedge that lie on the circle and . Let denote the area of the triangle and
let denote the measure of the angle at . Explain why someone would be interested in the value of: