@mathsy.io: Can you prove the derivative of sin x is cos x? An exam can ask you to, from first principles. Expand sin(x + h), split the limit, then let the unit circle show why sin h/h goes to 1 and (cos h − 1)/h goes to 0. Full film on YouTube, link in bio. #maths #alevelmaths #calculus #differentiation #trigonometry

✝️Simen08✝️ :

Prove-

sewer :

it follows trivially from the respective power series

ran :

wait why in radians and not degrees

FreeMathsTutorUK :

I’m glad you showed these arguments geometrically. Some people get wrongly upset when you use the small angle approximations and complain these are only obtainable through a Taylor Series and thus they think the argument is circular, but as you correctly show these small angle approximations can be derived without using a Taylor Series!

fizzzmattt :

Isn’t it obvious that cos(x)->1 when x->0? Just look at the graph :) And, about sin(x)/x, isn’t it proved fact, like, that’s e=lim(1+1/n)^n?

_lukasio__ :

the 2 limits you have used both use the fact that the derivative of sin is cosine in a way (Taylor’s expansion etc) so it’s not really a proof. The best way is using trigonometric identities

🇮🇹🐍•Saab 37 Viggen•🟨⬛️ :

Gerald_McDonald :

not the best demonstration

Tawhid :

😁😁😁