Consider an -sided regular polygon inscribed in a circle of radius Join the vertices of

Chapter 4, Problem 90

(choose chapter or problem)

Graphical Reasoning Consider an n-sided regular polygon inscribed in a circle of radius r. Join the vertices of the polygon to the center of the circle, forming n congruent triangles (see figure).

(a) Determine the central angle \(\theta\) in terms of n

(b) Show that the area of each triangle is \(\frac{1}{2} r^{2} \sin \theta\)

(c) Let \( A_{n}\)\) be the sum of the areas of the n triangles. Find \(\lim _{n \rightarrow \infty} A_{n}\)

Text Transcription:

Theta

\frac{1}{2} r^{2} \sin \theta

\lim _{n \rightarrow \infty} A_{n}