@@andeslam7370 I understand that. That teacher did it cuz he had some family issues and had to leave school for a week or so, so I think that decision proves that he is an excellent teacher.
This is one of those videos that has such a good visual representation and explanation of the idea its trying to convey that I instantly had an "aha!" moment.
The ancients of the past tried many times and found this " crazy" very logical structure to proove it. There are other ways to prove it, but they require more advanced mathematics...
I got the proof but the only question that I have is that crazy structure. How do you come up with it, I mean that structure seems random, I want to know the thought process of making that structure. If you can make a vid about it, it would be great.
So if you still are wondering, I'm pretty sure it all comes from the top line that creates the angle alpha + beta. The line between that one and the one at 0 degrees is just the angle that makes a right triangle from the point on the unit circle that line PO intersects with. The rest comes from that triangle.
@@thunderingeagle If I remember the contents of the video correctly, that would be because the hypotenuse is the radius of a unit circle, which just isn't drawn here. A unit circle has a radius of 1.
I proved this identity by considering the area of a triangle with the contained angle a+b. Splitting that triangle into two triangles with contained angles a and b respectively, then equating the sum of the areas of those triangles with the area of the triangle that they make up. Simplification gets me the result as desired.
@@anumwaseem7418 Does not matter. Consider any triangle ABC where the altitude from C to AB intersects AB at D. Denote angle ACD = a, and angle BCD = b. Then use the fact that area of triangle ABC = area of triangle ABD + area of triangle BCD.
@@ccbgaming6994what do you mean by x=1 what is x And to answer the question, no in the unit circle cos (beta) ≠ 1 That would mean for any triangle in the unit circle cos is always 1. That would destroy trigonometry. But, in the unit circle, cos(beta) does equal to adjacent side
Another way to prove it by using Euler formula (complex number) : exp(i*A) = cosA + i*sinA ---> exp(i*(A+B)) = exp(i*A)*exp(i*B) = (cosA + i*sinA)(cosB + i*sinB) = cosA*cosB + cosA*i*sinB + i*sinA *cosB +i*sinA *i*sinB exp(i*(A+B)) = cos(A+B) + i*sin(A+B) = cosA*cosB - sinA*sinB + i*(cosA*sinB + sinA *cosB ) ---> By equalizing the real and imaginary parts : cos(A+B) = cosA*cosB - sinA*sinB and sin(A+B) = cosA*sinB + sinA *cosB
It does not have to be 1 you can take any value for hypotenuse. 1 I usually taken because it is to calculate as 1x = x. Even if you take other values you will get the same answer. Like how 1/2 and 8/16 are the same but 1/2 is used more for convenience
I'm sorry, but this presentation falls short of proving the identity. The geometry of the diagram serves only to show that the relation holds for two positive angles that are each less than 90 degrees. There is no justification in the presentation as to why the relation holds for ALL pairs of angles (which, in fact, it does). To make such a claim without justification does nothing to instil a sense of reasoning into students' minds. Example: If I take the number 10 (an even number) and divide it by 2, I get 5 (an odd number). So, it must always be true that dividing any even number by 2 results in an odd number. This is patently nonsense, but I've used the same bogus logic as is used in this presentation. This clunky old proof is the same one my maths teacher trotted out 50 years ago. We did go on to show that the relation was, in fact true for all angles, but that required rather more work. But, why use this proof at all when there is a much more elegant proof available that uses simple co-ordinate geometry and doesn't suffer from the glaring shortcomings of the proof presented here, which should have been put out of it's misery years ago.
thanks!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Good job!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Great teacher!!!!!!!!!!!!!!!!!!!!!!!!
I regret not having a math teacher who can teach like you do. Good job Eddie
it's funny since our teacher couldn't teach for some reason, then he just link ur videos for us to self-learn XD
at least the teacher concedes. some do not and still firmly believe in their charisma despite all the counter evidences.
@@andeslam7370 I understand that. That teacher did it cuz he had some family issues and had to leave school for a week or so, so I think that decision proves that he is an excellent teacher.
Thanks for this video. I missed a day on my Year 13 Maths lesson and was utterly clueless. This video saved me no lie.
This is one of those videos that has such a good visual representation and explanation of the idea its trying to convey that I instantly had an "aha!" moment.
The ancients of the past tried many times and found this " crazy" very logical structure to proove it. There are other ways to prove it, but they require more advanced mathematics...
Omg, at the end I literally felt so happy that I started smiling, it felt such a big achievement. Lol😆😽
You’re a freaking life saver🖤🖤🖤
I got the proof but the only question that I have is that crazy structure. How do you come up with it, I mean that structure seems random, I want to know the thought process of making that structure. If you can make a vid about it, it would be great.
So if you still are wondering, I'm pretty sure it all comes from the top line that creates the angle alpha + beta. The line between that one and the one at 0 degrees is just the angle that makes a right triangle from the point on the unit circle that line PO intersects with. The rest comes from that triangle.
@@cftpafanOhh ok and why did we take the hypotenuse as 1 i.e OP ?
@@thunderingeagle If I remember the contents of the video correctly, that would be because the hypotenuse is the radius of a unit circle, which just isn't drawn here. A unit circle has a radius of 1.
@@cftpafan Man thanks a lot....thank you !!
@@thunderingeagle No problem at all, glad I could help!
that explanation was amazing, made my life easier
I proved this identity by considering the area of a triangle with the contained angle a+b. Splitting that triangle into two triangles with contained angles a and b respectively, then equating the sum of the areas of those triangles with the area of the triangle that they make up. Simplification gets me the result as desired.
What length did you choose for the sides of the triangle?
@@anumwaseem7418 Does not matter. Consider any triangle ABC where the altitude from C to AB intersects AB at D. Denote angle ACD = a, and angle BCD = b. Then use the fact that area of triangle ABC = area of triangle ABD + area of triangle BCD.
At 5:36 on that triangle with cosb and sinb doesnt that prove sin^a + cos^a = 1 ?
Sin^a and cos^a =???
_Did you mean_ : sin^2 theta + cos^2 theta = 1
Because it does prove that
Which book is this?
i don't know if you still need it, but i came across this problem from titu andreescu's "103 trigonometry problems"
Thank you so much this was super helpful!!!!!
It is quite easy to solve with unit circle!
At 0:45 , how is that thing an identity?
Because it is…
@@ccbgaming6994 shit...now I m seeing...
I saw LHS as 1×1 ....but it is |x|
😅😅
@@manasraj5640 Oh lol
@@manasraj5640same
Proof sin(a+b) in unit circle taking (a+b) greater than 90 degree
Wish if I had a teacher such as you.
what side of the triangle would cos(a+b) be then?
th-cam.com/video/V3-xCPDzQ1Q/w-d-xo.html Khan Academy Proves it for cos(a+b)
In what year of school do u have to learn this?
Alex Dias 11
Depends on the country and system. I'm learning it in year 12
What software is he using with his stylus? Works better than mine.
The software I have no Idea. But that's an iPad pro and an Apple Pencil
Notability
Which class he is teaching
if its in a unit circle isn't cos(beta) just 1? why can't we consider it 1?
Only if x equals 1
Because the hypotenuse is always 1 for a unit circle
@@ccbgaming6994what do you mean by x=1 what is x
And to answer the question, no in the unit circle cos (beta) ≠ 1
That would mean for any triangle in the unit circle cos is always 1. That would destroy trigonometry.
But, in the unit circle, cos(beta) does equal to adjacent side
Another way to prove it by using Euler formula (complex number) : exp(i*A) = cosA + i*sinA --->
exp(i*(A+B)) = exp(i*A)*exp(i*B) = (cosA + i*sinA)(cosB + i*sinB) = cosA*cosB + cosA*i*sinB + i*sinA *cosB +i*sinA *i*sinB
exp(i*(A+B)) = cos(A+B) + i*sin(A+B) = cosA*cosB - sinA*sinB + i*(cosA*sinB + sinA *cosB ) --->
By equalizing the real and imaginary parts : cos(A+B) = cosA*cosB - sinA*sinB and sin(A+B) = cosA*sinB + sinA *cosB
why OP length should be equal to 1
only doubt i had in this video
i hope u clear this soon sir
It is 1 because it is a given, he says so in the beginning.
@@EliasGuderian it is a proof we should take 1 and we should do
is there no alternatives
there should not be any numbers assigned in proofs i think so
@@jyothieswar5575 its because it is a radius of the unit circle
It does not have to be 1 you can take any value for hypotenuse. 1 I usually taken because it is to calculate as 1x = x.
Even if you take other values you will get the same answer.
Like how 1/2 and 8/16 are the same but 1/2 is used more for convenience
Thank you
thanks
I'm sorry, but this presentation falls short of proving the identity. The geometry of the diagram serves only to show that the relation holds for two positive angles that are each less than 90 degrees. There is no justification in the presentation as to why the relation holds for ALL pairs of angles (which, in fact, it does). To make such a claim without justification does nothing to instil a sense of reasoning into students' minds. Example: If I take the number 10 (an even number) and divide it by 2, I get 5 (an odd number). So, it must always be true that dividing any even number by 2 results in an odd number. This is patently nonsense, but I've used the same bogus logic as is used in this presentation. This clunky old proof is the same one my maths teacher trotted out 50 years ago. We did go on to show that the relation was, in fact true for all angles, but that required rather more work. But, why use this proof at all when there is a much more elegant proof available that uses simple co-ordinate geometry and doesn't suffer from the glaring shortcomings of the proof presented here, which should have been put out of it's misery years ago.
Could u tell where the more elegant proof is? I couldn't find any good ones on TH-cam.
@@stupidlyidiotic3592 Hi I assume it is this. courseware.cemc.uwaterloo.ca/web/Gr12AdFu000/Public_Html/slides/TIE/CompoundAngleFormulas.pdf
thanks!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Good job!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Great teacher!!!!!!!!!!!!!!!!!!!!!!!!
अच्छा समजाते है aap
English me likho tab samaj ayega usse
thanks!!!!!!!!!!!!!!!!!
Eddie wow not eddie woo lol
Damnnnnnnn!!!!!!!!!!!!!!!!!!
आप