I really don't like Math, but Mr. Woo's teaching caught my attention and sparked my interest in the subject. Not only this, he also seemed to capture my heart bit by bit the more I watch him. Lol! Kidding aside, the way he teaches here is perfectly clear and easy to understand. Impressive teaching. Your students and the school where you are teaching are lucky to have such a brilliant mind like you.
12:48 Pythagorean Theorem: Enhanced Edition now available on all consoles! err.. triangles! lol Your videos are helping me understand math much much better, especially trig. You're the best teacher ever! Thank you very much!
Nice technique in showing the formula of law of cosines. However, in the part of your video 12:30-12:37; why do you need to swap b to c? Students in other institution may get confuse with that. Instead of replacing b to c, why not let b^2 be transpose on the left side of the equal sign and let the formula be like this: b^2=a^2+c^2- 2ac (cos B) In that case, there will be no confusion among students at the same time there will no more question, why "b replaced c." Because replacing b to c is illogical. Why not stop there and arrange everything as I have shown.
I believe he did this because he wanted students to observe the connection between law of cosines and the pythagorean theorem. this is easiest for students to see when written as c^2 = a^2 + b^2 - 2ab*cos(C). If our goal is to have the final statement be in this form, perhaps a better approach would be to just swap the position of c and b in the initial diagram, and then you will end up with the preferred form at the end without needing to do that last step at the end where you algebraically swap b for c and c for b
Agreed. You can actually derive all 3 using the same technique he used to solve for C^2. However, i have yet to find someone on RU-vid who does it... The way it is taught here does not reflect textbooks at all.
Thanks for sharing! I posted a short video on deriving the law of cosines, It should apply for all angles (acute, obtuse, reflex, negative). Hope to get your thoughts.
It's not you. He does some strange stuff here that doesn't happen in textbooks and this doesn't reflect whats in the textbook definition of law of cosines. He might have just gotten it wrong. Best to use lesson notes when teaching to mitigate this problem. However, I do agree that he is an AMAZING teacher. And I strive to be like him. He is a great role model!
basically, since the variables 'B' and 'C' are arbitrary, he switches them. if he wanted to he could have changed his diagram as well to replace b and c. he is saying the same thing, just as if he had labeled the sides differently at the beginning. since the variables are representative, it doesn't matter what he chooses, which justifies switching them up.
@@You-bb5wo Just draw the initial triangle and rename the sides as you like. The name you give to all the angles and sites is arbitrary as long as you name them consitently i.e. dont name two sites the same which are not the same etc. and change the name/variable in all formulas.
