Hello! Thank you for your very clear explanation, i have a question: this proofs seem true only when alfa and beta are acute angles. How to prove that they hold for any alpha and beta (even negative or 188 degrees or 520 degree or any other angle)?
Great question. These kinds of geometric proof don’t prove the case for angles > 180 directly but you can use other identities like sinx = sin (180-x). Eg if you have sin(150-x) it’s equivalent to sin(30+x) or sin(230-x)=sin(-50+x). I think that should be enough to extend these proofs.
@@mathonify Thank you for the answer, but at that point one could ask: "ok but how to prove the other identities?" I think the true starting point (of the other identities too) is taking the distance between any two point on the goniometric circumference and proving cos(x+y) = cos x cos y - sin x sin y. Then from there gaining all other trig formulas whatsoever
@@mathonify No, you lost me. You left out too many lines. I can get to Sqrt 2•Sqrt 3 /4, but how you got a +1 baffles me. On top of that, when I plug in sin 75 (0.96592...) and plug in the values into your equation, I dont come up with the same figure...
Correction. Using the method similar to that one of using " a quadrilateral = 360 " I got a result of A+B. However, when I used the method of summing all the angles along the upper horizontal line of the square, I got the correct angle of A.
Before seeing this video I had envy on trigonometry but now it's my favourite I don't know how much times I can thank you. To me you are a math guardian angel
@@mathonify The eq is a little different from those, taking tan^-1 on both sides only give two out of four solutions. Using the formula tan2u when there is (2x - 84 deg)? Does that work?
it is a decently logical challenging subject, trig, but the more you get into it, it changes into an academical damping machine how about some trig function of 16.4976 so you can see these tricks are boring meaningless stuff, plays with easy radian degree of 35, 45, 60, etc human build calculator for this, you are not studying for becoming a human calculator
Great video. Thank you 👍
Hello! Thank you for your very clear explanation, i have a question: this proofs seem true only when alfa and beta are acute angles. How to prove that they hold for any alpha and beta (even negative or 188 degrees or 520 degree or any other angle)?
Great question. These kinds of geometric proof don’t prove the case for angles > 180 directly but you can use other identities like sinx = sin (180-x). Eg if you have sin(150-x) it’s equivalent to sin(30+x) or sin(230-x)=sin(-50+x). I think that should be enough to extend these proofs.
@@mathonify Thank you for the answer, but at that point one could ask: "ok but how to prove the other identities?" I think the true starting point (of the other identities too) is taking the distance between any two point on the goniometric circumference and proving cos(x+y) = cos x cos y - sin x sin y. Then from there gaining all other trig formulas whatsoever
Excellent explanation
Heya, at 2:43, you could explain how you got √2 (√3+1)/4? I'm kinda confused.
have a go at plugging in the exact values of sin45, sin30, cos45 and cos30 into the line above. I skipped a few lines of working out
@@mathonify No, you lost me. You left out too many lines. I can get to Sqrt 2•Sqrt 3 /4, but how you got a +1 baffles me. On top of that, when I plug in sin 75 (0.96592...) and plug in the values into your equation, I dont come up with the same figure...
@@mathonify Got it. At 22.18 in the evening, the neurons start slowing down. I see you factored out the sqrt 2.
I know that you have to know exact trig values for GCSE but do you need to Know this as well ?
No this is a level I updated the title now
Thanks
Hey, At the 16:56 mark, you solved that angle and said it is A, how is that possible? Also, I solved it to be A+B
Correction. Using the method similar to that one of using " a quadrilateral = 360 " I got a result of A+B. However, when I used the method of summing all the angles along the upper horizontal line of the square, I got the correct angle of A.
Yes I would use the angles on the straight line to get angle A in that case. Not sure why I said “similar idea”.
@@mathonify Thank you. Great video.
Thank you so much
Before seeing this video I had envy on trigonometry but now it's my favourite I don't know how much times I can thank you. To me you are a math guardian angel
thank
What if you got tan(2x - 84deg)=0? Nobody even teaches stuff like this...
This is a trigonometric equation that you need to solve. See my video on solving trig equations: th-cam.com/video/kajoHHenS2Q/w-d-xo.html
@@mathonify The eq is a little different from those, taking tan^-1 on both sides only give two out of four solutions. Using the formula tan2u when there is (2x - 84 deg)? Does that work?
This Soo helpful
Tnx alot ..
it is a decently logical challenging subject, trig, but the more you get into it, it changes into an academical damping machine
how about some trig function of 16.4976
so you can see these tricks are boring meaningless stuff, plays with easy radian degree of 35, 45, 60, etc
human build calculator for this, you are not studying for becoming a human calculator