Sine of a Sum I (visual proof; trigonometry)

This is a short, animated visual proof of the sum formula for the sine function using the Side-Angle-Side triangle area formula. This theorem relates the sine of a sum to the sum of products of sines and cosines. #mathshorts #mathvideo #math #trigonometry #sine #sinofsum #triangle #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #circle #sideangleside #trianglearea

To learn more about animating with manim, check out:
____________________________________________________
Background music:
Creative Commons Attribution 3.0 Unported License

[LUMEN_science]

triangles are always interesting! Congratulations!

[omerhamzasacan]

You are amazing, I wished my teacher was like you.

[Vengemann]

This was straightforward perfectly described clear and very simple derivation thanks 👍 :)

[galaburdakirill]

among all the proofs the one is the easiest to memorize, thank you

[adwz]

This is great, such a simple way of deriving this! I was wondering how we get to cos(a+b) using a similar method, but we could just take a -> pi/2 - a and b -> -b in the sin(a+b) formula. I wonder how this would look visually

[MATHSTATION]

Very nice.
Which software do you use for making such kind of amazing animation?

[overlord]

best derivation of sin(a+B) on the internet

[hantinvu]

very smart ❤
i don't know the simplest way but using Euler's formula and imaginary number <333
thanks so much

[yashrawat]

Nice prove, although it would do some weird things when considering over whole Real Domain

(0, PI/2) is the best

[piyush.bhumi]

Love from india sir ❤, I have only found your video on youtube regarding my Problems sir great respect from the bottom of my heart

Edit-I am in class 10th sir

[SimeonAndréJohansenPAKV]

I'm very new to learning this concept, so I maybe missed something, but doesn't this proof mean that sin (a+b) also could equal = sin(a)cos(a)+cos(b)sin(b) (which it doesn't). Why is the y value put on the opposite trangle? What am I missing? Thanks for answer.

[hammadullahshaikh]

Plz why y interchanging y for opposite sides

[russellmanning]

You miss a lot of steps. I wonder how many people can fill in these steps

[KenshinMutaito]

something is missing, , the first formula to derivate the others so it's uncomplety. but welld one.