what is the meaning of taylor series

[serimc]

meaning of taylor function

Hi
we know the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

But in taylor series there is a differnet explanation ( https://mathworld.wolfram.com/TaylorSeries.html ).I can't relate between trigonometric meaning and taylor series meaning of functions(for example sin,cos,e...).
What are the differences?or are they same?
I really confused.
Can you please explain the meaning of taylor series.
Thanks

 

[mahematician]

hi



taylor series is a fundamental concept in analysis and the beauty of it is with the help of it we can represent any trigonometric function in terms of algebraic expansions( that is in terms of polynomial expansions or series) .


AS we know that trigonometric functions are transcendental functions taylor series give the expansion of transcendental in to algebraic form.


also with the hep of taylor series we can tell whether a given function is analyic or not with out using any other mathods.

 

[serimc]

thanks mahematician
you said:
"taylor series is a fundamental concept in analysis and the beauty of it is with the help of it we can represent any trigonometric function in terms of algebraic expansions( that is in terms of polynomial expansions or series)"

Actually i don't understand this part.How did taylor find it?What is the magic behind this series.Where does this serie come from (its mathematical roots).

 

[bmwcoupe]

Added after 18 seconds:


hi
there is taylor series and you should not forget that there is also
maclouren series around zero..

https://en.wikipedia.org/wiki/Taylor_series

and there is also laurent series for complex's functions, it takes you to
a places where taylor's series can not rich ...

https://en.wikipedia.org/wiki/Laurent_series

good luck
bmw man.