# example of Taylor polynomials for $\sin x$

## Primary tabs

Keywords:
Taylor polynomial, pretty graphs, sine function
Major Section:
Reference
Type of Math Object:
Example
Parent:

## Mathematics Subject Classification

41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)

### graphs

oh I mistook polynomials and series on the correction, nevermind.

I quite like your graphs, the look is Mathematica-ish to me, and if so, what are the parameters you used for Plot?
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

### Re: graphs

Yep, the graphs were made with Mathematica,

* To find the Taylor polynomial of degree $n$

Normal[Series[Sin[x],{x,0,n}]]

* To plot (for example Sin[x] and T_1(x)=x ):

Plot[{Sin[x],x},{x,-4,4},ImageSize->{640,480},PlotStyle->{Hue[0.2],Hue[0.7]}]

I can't remember the Hue assignment for the colors I used. The color is given by a number 0<=x<= 1 and Hue[x].

* To export the graph to eps, jpg or whatever .ext :

Export["prettygraph.ext", Plot[{Sin[x],x} ... ]]

Alvaro

### Re: graphs

thanks a lot, I was wondering of Hue , since I always used RGB which is too cumbersome, I forgot you could export directly from code, thanks again
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f