TR-41: Half Angle Identities (Trigonometry series by Dennis F. Davis)
Vložit
- čas přidán 29. 12. 2021
- Algebraic and Geometric proofs of the Half-Angle Identity.
Series introduction including complete video list:
TR-00: [ • TR-00: Introduction to... ]
International A level, Intl A Level, IAL, Edexcel, Pearson exam board, CIE, Cambridge exam board, P3, P2, Year 10, Class 11
I just started studying grade 11 and I'm glad i found your videos, the visual proofs are amazing, they just sink into me, the formula's are so easy to remember!
What a time to be in, I don't feel dissapointed anymore that 10th grade 2021 board exams were cancelled due to the pandemic and not the 2022 one.. cause i just recieved something way better ^^
What a nice thing to say, thank you!
wow, i just love this series. It helps to understand theese complicated topics so fast, it’s really awesome. I‘m sure this is going to be a big success :)
FR
Quality videos
Straight forward
brilliant, I used this many times in my algorithms and today I know why ;P
6:50 - I'm not exactly sure how you derived cos(theta/2) as 2 sides for the two right triangles within the isosceles. I understand why the entire isosceles hypotenuse side is equal to 2cos(theta/2), But since you divided the isosceles into two right angles, the formula used for either should be ADJ_SIDE = hypotenuse*cos(theta/2). or 1 * cos(theta/2). specifically because the side solved for is adjacent to
Thanks Brandon.
I want to be helpful, but I'm not sure I understand where we're disconnected. We agree that the hypotenuse of the big gray triangle is 2cos(θ/2). So each half must be cos(θ/2), and you correctly state the formula used for this: ADJ_SIDE = hypotenuse*cos(θ/2). So it sounds like we both nailed it and that's why I'm not sure what your question is. I'll try again if you clarify, but it sounds to me like you got it.
It seems to me that the (beatiful) Thale´s theorem is a special case of the Inscribed angle theorem. Do you think the same?
Yes I agree with you. The central angle (diameter) would be π radians, and every corresponding inscribed angle would be half that: π/2 radians, or a right angle.
@@DennisDavisEdu Exactly, thanks. Enjoying your videos
Geometrifying Trigonometry
I have made a language (parser /compiler/lexical analyser)which takes trigonometry expression as input
And
Converts that to euclidean geometry
Then
It searches hidden truths from geometry
Automated theorem prover
Geometrifying trigonometry
Is the formal language which is cross platform communicator
Platform 1 is trigonometry ecpression in latex or excel format
Platform 2 is euclidean geometry
My system is formalized language and framework to do this
I am sure you get this question all the time, but, may I ask what software you use to create these wonderful videos? I would welcome an answer from anyone. And Thanks, your videos have saved my life (high school math teacher).
I use Microsoft Powerpoint with the "morph" transition to create the animated parts.
Very cool sir❤️, sorry what program do you use for the explanation?
Microsoft PowerPoint with the morph transition for the animations.
Thanks for watching!
Thanks 😊
9:04 I don’t understand how to get 2sinhalftheta ? Could you explain it to me please?
Considering the big triangle, the hypotenuse is 2 since it has 2 radii each of length 1.
The angle on the left side of the diagram is ϴ/2 (by the inscribed angle theorem).
So the side Opposite ϴ/2 is sin(ϴ/2) times the hypotenuse (2). (see TR-17 if not clear)
So 2sin(ϴ/2).