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Area of a Sector of a Circle: Proof
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 r^2*θ. 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!
Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!103419&authkey=!ADTcnCJDE-RQbwk&ithint=file%2cpdf
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/area-of-a-sector-of-a-circle-proof
Related Videos:
Equation of a Circle and it's proof: http://youtu.be/xMXYJ9UeF4I
Trigonometry: Sine, Cosine and Tan Functions: http://youtu.be/WKTIlF2oWw8
Exact Trigonometry Ratios Part 1: 0, 30, 45, 60, and 90 Degrees: http://youtu.be/ln03a5KvQAY
Trigonometry Identities: Proof that sin^2(x) + cos^2(x) = 1: http://youtu.be/o-fAx_96lgw
Inverse Trigonometric Functions: Inverse cosine, sine, and tan Functions: http://youtu.be/Ifv1vkJZdrk
Trigonometry Identities: sin(-x) = - sin(x) and cos(-x) = cos(x): http://youtu.be/tD5EA2SXyFQ
Trigonometry Identities: cos(2π + x), sin(2π + x), cos(π/2 -x), sin(π/2 -x): http://youtu.be/EynSefQs308
Trigonometric Substitution for Integrals: http://youtu.be/2pWvGXwtVJo
Trigonometric Substitution for Integrals: One to One Function: http://youtu.be/QO26MkCC3eU
Simple Proof of the Pythagorean Theorem: http://youtu.be/yt-EJlbJQp8
Trigonometric Integrals: Integral of cos^2(x): https://youtu.be/uuWIDgQ8NsY
Download the notes in my video:
Related Videos: .
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