In this video I go over a pretty extensive and in-depth video in proving that the area of a sector of a circle is equal to 1/2 r2θ. This formula works for any angle in the circle. The proof involves first considering a sector that is at most a quarter of a large circle and breaking it into two areas: a triangle and a curved section. The area of the curved section requires trigonometric substitution for integrals and as well as a good understanding of trigonometric functions in general to evaluate. Although this video is almost an hour long, it brings together many different concepts of mathematics in finally deriving a very short and concise formula for the area of a sector of a circle, thus this video is a important video to watch!
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