TI-M: e^x, sin x, cos x


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TI-M: e^x, sin x, cos x




I know one definition of e^x is:
e^x = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ... + x^n/n! + ...
      = 1 + x + x^2/2 + x^3/3! + x^4/4! + ... x^n/n! + ...

Similarly, sin x and cos x can be defined by an infinite sum:
sin x = x - x^3/3! + x^5/5! - x^7/7! + x^9/9! - ...
cos x = 1 - x^2/2 + x^4/4! - x^6/6! + x^8/8! - ...

Does anyone know any proofs of these?  I sort of remember the e^x infinite 
sum coming from the definition of e, but I can't seem to recall it and don't 
want to bother finding it ;)

Thanks for the insight,

JayEll

P.S.:  I'm not 100% sure these infinite sums are correct; they're coming from 
memory, so correct them if they're wrong...



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