Theorems about triangles | Trigonometry

Law of cotangents

In trigonometry, the law of cotangents is a relationship among the lengths of the sides of a triangle and the cotangents of the halves of the three angles. This is also known as the Cot Theorem. Just as three quantities whose equality is expressed by the law of sines are equal to the diameter of the circumscribed circle of the triangle (or to its reciprocal, depending on how the law is expressed), so also the law of cotangents relates the radius of the inscribed circle of a triangle (the inradius) to its sides and angles. (Wikipedia).

Law of cotangents
Video thumbnail

Trigonometry X: the Law of Cotangents (and another lovely relation involving cotangents!)

Boy, oh boy this is a longish one. I prove the Law of Cotangents using the incenter of the triangle, after motivating the path with another way one might seek to prove the Law of Sines using the circumcenter of the triangle. After that, I demonstrate an equally lovely relationship betwee

From playlist Trigonometry

Video thumbnail

Trigonometry 8 The Tangent and Cotangent of the Sum and Difference of Two Angles.mov

Derive the tangent and cotangent trigonometric identities.

From playlist Trigonometry

Video thumbnail

Trigonometry 5 The Cosine Relationship

A geometrical explanation of the law of cosines.

From playlist Trigonometry

Video thumbnail

Proof - The Derivative of Cotangent: d/dx[cot(x)]

This video proves the derivative of the cotangent function. http://mathispower4u.com

From playlist Calculus Proofs

Video thumbnail

Simplifying an expression raised to a rational power

👉 Learn how to simplify rational powers using the power and the quotient rules. There are some laws of exponents which might come handy when simplifying expressions with exponents. Some of the laws include the quotient law which states that the quotient of numbers/expressions having the sa

From playlist Simplify Fractional Exponents using Power to Quotient

Video thumbnail

Simplify an expression

👉 Learn how to simplify rational powers using the power and the quotient rules. There are some laws of exponents which might come handy when simplifying expressions with exponents. Some of the laws include the quotient law which states that the quotient of numbers/expressions having the sa

From playlist Simplify Fractional Exponents using Power to Quotient

Video thumbnail

Derivative of cot(x)/sin(x)

Derivative of cot(x)/sin(x)

From playlist Random calculus problems:)

Video thumbnail

Applying the law of cosines when given SAS

Learn how to solve for the lengths of the sides and the measures of the angles of a triangle using the law of cosines. The law of cosines is used in determining the lengths of the sides or the measures of the angles of a triangle when no angle measure and the length of the side opposite th

From playlist Law of Cosines

Video thumbnail

Using the law of cosines for a triangle with SAS

Learn how to solve for the lengths of the sides and the measures of the angles of a triangle using the law of cosines. The law of cosines is used in determining the lengths of the sides or the measures of the angles of a triangle when no angle measure and the length of the side opposite th

From playlist Law of Cosines

Video thumbnail

Trigonometry IX: the Law of Tangents (and a lovely little tangent identity!)

I prove the Law of Tangents using the previously demonstrated Law of Sines, and follow that up with a neat treat also involving tangents! If you have any questions, feel free to leave a comment or email me at the incorrectly spelled whatthehectagon@gmail.com Don't forget to like, subscri

From playlist Trigonometry

Video thumbnail

What is a Tensor 15: Coordinate Transformations

What is a Tensor 15: Coordinate Transformations

From playlist What is a Tensor?

Video thumbnail

Noether's theorems and their growing physical relevance by Joseph Samuel

DATES: Monday 29 Aug, 2016 - Tuesday 30 Aug, 2016 VENUE: Madhava Lecture Hall, ICTS Bangalore Emmy Noether (1882­-1935) is well known for her famous contributions to abstract algebra and theoretical physics. Noether’s mathematical work has been divided into three ”epochs”. In the first (

From playlist The Legacy of Emmy Noether

Video thumbnail

Seminar In the Analysis and Methods of PDE (SIAM PDE): Alexander Kiselev

Title: The Flow of Polynomial Roots Under Differentiation Date: Thursday, June 2, 2022, 11:30 am EDT Speaker: Alexander Kiselev, Duke University Abstract: The question of how roots of polynomials move under differentiation is classical. Contributions to this subject have been made by Gaus

From playlist Seminar In the Analysis and Methods of PDE (SIAM PDE)

Video thumbnail

The Tangent (T) Scale

This is a video about the Tangent (T) Scale on the slide rule. If you haven't watched my video from the basic slide rule series that covers the T (& S/L) scale, then you may want to watch that first. You may also want to review my video on the S Scale beforehand. Slide Rule Playlist (star

From playlist All Slide Rule Videos

Video thumbnail

Rigidity and recurrence in symplectic dynamics - Matthias Schwarz

Members’ Seminar Topic: Rigidity and recurrence in symplectic dynamics Speaker: Matthias Schwarz, Universität Leipzig; Member, School of Mathematics Date: December 11, 2017 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Basic slide rule theory and use (Part 5): Chaining and S/T/L scales

The fifth (and final) of a series of videos explaining the basic slide rule. This video explains how to chain operations and how to use scales S, T, and L. Basic slide rule playlist: https://www.youtube.com/playlist?list=PL_qcL_RF-ZyvJYtIr9NRXJX958d6BgdbN All my slide rule videos: https

From playlist Basic slide rule theory and use

Video thumbnail

Trigonometry For Beginners!

This math video tutorial provides a basic introduction into trigonometry. It covers trigonometric ratios such as sine, cosine, and tangent. It explains how to evaluate it using right triangle trigonometry and SOHCAHTOA. In addition, it explains how to solve the missing sides of triangle

From playlist Pre-Algebra Video Playlist

Video thumbnail

Derivative Functions: Quotient Rule with Trigonometric Functions

This video explains how to determine a derivative function involving cotangent using the quotient rule.

From playlist Differentiation Using the Quotient Rule

Video thumbnail

13. EFT with Fine Tuning

MIT 8.851 Effective Field Theory, Spring 2013 View the complete course: http://ocw.mit.edu/8-851S13 Instructor: Iain Stewart In this lecture, the professor discussed 2-nucleon nonrelativisitic EFT, bubble sums & effective range expansion, fine tuning from RGE flow between fixed pts, and

From playlist MIT 8.851 Effective Field Theory, Spring 2013

Related pages

List of trigonometric identities | Law of sines | Mollweide's formula | Law of cosines | Heron's formula | Triangle | Law of tangents | Circumscribed circle | Trigonometry | Proofs of trigonometric identities