let me copy and paste that so do we see any relationship between these approximations? so before, you probably would have guessed there's some relationship between cosine and sine but what about e^x? so what you see here is that cosine(x) looks a lot like this term plus this term, although we probably want to put a negative out front here so we have a negative version of this term right here plus this term right here plus a negative version of this term right over here and sine (x) looks just like this term plus a negative version of this term plus this term plus a negative version of the next term so if we could somehow reconcile the negatives in some interesting way it looks like e^x at least the polynomial representation of e^x is somehow related to a combination of the polynomial representations of cosine of x and sine of x so this is starting to get really really really cool we're starting to see a connection between something related to compound interests or a function whose derivative is always equal to that function and these things that come out of the unit circle and oscillatory motion and all kinds of things there starts to seem a kind of pure connectiveness there. but i'll leave you there on that video and in the next video