TR-33Z: All Trig Functions on the Unit Circle (Trigonometry series by Dennis F. Davis)
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- Опубліковано 20 вер 2024
- Representations of the magnitude of all six trig functions are shown on a unit circle. The assertions are proven using the properties of Similar triangles. Additionally, the Pythagorean Identities are shown to be represented by triangles on this diagram.
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've always heard "sine" "cosine" nd other stuff are just "ratios that you need to memorize". But this diagram just explains it all. Like how they just put the prefix co- for every line in the opp direction to the main line and how the big formulas were derived. All of it depicted in seconds. It amazing bro, love you
I love him too :) Watch me get my A in Precalculus in a month :)
Man, this is too cool. I knew there had to bee more to it. Wonder why schools decide to teach the way they do.
ikr, their way is both incompetent and inefficient. Why the hell they even adopt it
Algebra is a good way of confusing people when you are trying to teach trig. The maths teachers probably avoid it when explaining it to their own children. The teachers are given a curriculum and have to teach it as instructed. The internet has taken this out of their hands. I was told the intention is to keep all the students at the same level.
My teacher showed us this video in class. I live in Barcelona, Spain.
@@Cono10YT your teacher is great. Lucky you ✌️
@@Cono10YT How interesting! So I'm now an international UA-cam personality!
Yours is the ONLY video that explains all of these so clearly. Also I was VERY confused about why tan line was shown in two different ways. You made it a point to explain that also🙏.... Not enough words to say thank you. ❤️❤️❤️❤️❤️After so many years of learning trigonometry, finally it makes sense. Thank you again.
I was always confused about these functions, but after watching your video, everything became clear. Thank you sir. And thank God that I found your channel❤....
This is a great video. It’s helping me visualize in how to coordinate this concrete slab I have to lay out at work.
Professor Davis your videos are son neat and beautiful and your explanation spotless. I hope you keep uploading more and more enlightening classes. Congratulations and thanks
Your analysis was illuminating!
you deserve loadsa views. keep going please..
You are doing well.just keep it up.
Thank you so much. Elegance par excellence.
The half roof slope length (cotangent) of my house is equal to the half length ceiling (cosine) of my house divided by the height of the house wall (sine). To think of it in practical terms. Looks like a half house to me.
Most is very nice. :-) But in the animation, abozt 6:45, it's not clear how one can see that the value of tan is now negative.
get an A 2 size paper and draw the lot on a circle. The object is to show the calculations for finding the coordinates and, or angles from any two variables and be able to draw and show them on a circle. Then you have mastered the maths. Then you have to apply them to nature. For example, the resonance distance of a sound wave that produces an echo for the science of acoustics, or the art of music.
OMG This video made my trig paper so much easier. TYSM
RESPECTED SIR, YOU ARE GOD OF TRIGONOMETRY 🙏 !!!!....
Hello, I absolutely love your videos. I am curious, what software do you use to animate the math?
Hi File, thanks for your viewership!
I mostly use painstakingly-crafted PowerPoint with the morph transition to provide the animations.
The only trigonometry video that gave me goosebumps 😂😂😂. ❤🌹✌️
Talk about seeing things in a new light. The trig functions are so much more real when you see them displayed like this. Also Makes it WAY easier to remember the domain and range of these functions
I agree Tim, this construction makes a lot of trig seem clearer. Thank you so much for all of your nice comments, I read them all!
Brilliant Trig teacher
Sooooooooo useful!!!
Hi Dennis.Thanks for the wonderful videos. i was just wondering how you determine dsecant and cosecant as purple and pink lines on the graph?
I'm not sure I understand the question, it's in this video at 3:43, right?
@@DennisDavisEdu Yes exactly.I didn't understand as to how the purple line is made as secant and pink line as cosecant on the graph.
It's shown with similar triangles:
Purple over Yellow equals Yellow over Blue. Purple over Yellow is Purple since Yellow is 1. Yellow over Blue is 1/cos. That's the definition of Secant so Purple equals Secant.
Pink over Yellow equals Yellow over Red. Pink over Yellow is Pink since Yellow is 1. Yellow over Red is 1/sin. That's the definition of Cosecant, so Pink equals Cosecant.
Please and please compond angle double angles and half angles proof like this .best way
Yes I will cover those topics in future videos.
I was going to finish the entire series before I published any, but I've completed to about TR-34 or TR-35 and decided to publish what I had ready. So videos after these will not come out as frequently because I'm all caught up with what I've been working on the past 2 years.
@@DennisDavisEdu what have you been working on for the part 2 yrs...? very intriguing. What is it?
this is now where near all the trig functions
could you please do one for Sgn(x), Si(x), Sin(z), Cos(z), Tan(z), Cosh(x), Tanh(x), Sinh(x), Sech(x), Csch(x), Coth(x), ArcSin(x), ArcCos(x), ArcTan(x), ArcCsc(x), ArcCot(x), ArcSec(x), ArcSinh(x), ArcCosh(x), ArcTanh(x), ArcCsch(x), ArcCoth(x)?
Sir, just a quick question. You show the identities in the actuate angle situation , saying, 0
All of the identities covered in TR-33 through TR-41 are true for all angles, acute and obtuse. The exception would be they are not true for angles where one of the terms is undefined. For example, tanθ = sinθ/cosθ is always true EXCEPT where cosθ = 0.
I use acute angles when proving the identities geometrically because they are more convenient to see and draw, but the identities can be generalized to all angles.
Thanks for watching and for your kind comments!
How can you have a theta greater than 90 deg in a right angle triangle? It'd break the 'Angle sum property' of a triangle you know.
@@maninimahapatra649 See video TR-14: ua-cam.com/video/oJgBJfstOOU/v-deo.html
Awesome!!
I love this video ❤️
6:28 "..the relationship between sine and secant, how they just touch at the quadrantal angles." I am unable to see this. Were you referring to the reciprocal relationship between sine and *cosecant, because their graphs touch when both of them are 1 at θ = nπ + π/2.
You are right! I misspoke in the video. The "just touching" relationships occurs between [sine and cosecant] and [cosine and secant]. Thank you for paying such close attention!
This Asian dude givin me the vibes now lmaoo 😂😂😂
A genius pro gamer vibes
Thanks many 👍💞💞💞💞
I had this silly question at 3:17 and 4:09
that How can we prove both are similar triangle?
If we can show that two triangles have two common angles then they must be similar. All of the triangles in this video are similar to each other: They all have a right-angle of course and the other two angles are θ and the complement of θ.
At 3:17, the topmost (smallest) angle in the "cotangent" triangle is the complement of θ. In the lower left corner of the coordinate system (at the origin) you can see that this angle plus θ is a right angle so it's complementary to θ.
For the other triangle (that has sin and cos) you can see its angle at the yellow dot. It's in a right triangle across from angle θ, so it must also be complementary to θ.
There aren't any other angles in the whole diagram. Every angle is either a right angle, θ or θ's complement.
@@DennisDavisEdu Oh yup!! I am so grateful for your reply! You are a great teacher! Thank you🙏😀
thank you Denny. sir I love you and I love math as well.
i knew there had to be more to trig :)
Супер 😊
Спасибо за ваш приятный комментарий!
And graph one by one animation
Maravilha
Obrigado!
why this isn't taught in every trig class......
I saw the sign and it open my mind i saw the light (ace of base)
Just punch the "Demo" key on any old Casio keyboard and you've got an Ace of Bass song! I'm glad my video opened your mind.
goshh i hate myself, in all of the videos about trig functions, i can't still understand!!
the only functions that i understand is sine and cosine; and the rest is confusing!!
Try this video. It helped me a lot. It's only 8 minutes long.
ua-cam.com/video/Dsf6ADwJ66E/v-deo.html
by youtube algorithm I accidently watched the animation first, now I'm watching the proving/proof part. it all makes sense.
This guy talks to fast to be taken seriously also he says "dont" alot something real educators avoid doing.