Taylor expansion

Taylor expansion and approximation with Taylor polynomials of functions, including a cubic function (y=(x+1)*(x-1)^2=x^3-x^2-x+1), sine, cosine, as well as their relative error.

For more on the small-angle approximation, please see the “Taylor expansion” tag . For more on the pendulums, please see the “pendulum” tag.

Edit and compile if you like:

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% Author: Izaak Neutelings (November 2020)
\documentclass[border=3pt,tikz]{standalone}
\usepackage{amsmath} % for \dfrac
\usepackage{physics,siunitx}
\usepackage{tikz,pgfplots}
\usepackage[outline]{contour} % glow around text
\contourlength{1.0pt}
\usetikzlibrary{angles,quotes} % for pic (angle labels)
\usetikzlibrary{arrows.meta}
\usetikzlibrary{decorations.markings}
\tikzset{>=latex} % for LaTeX arrow head
\usepackage{xcolor}
\colorlet{xcol}{blue!60!black}
\colorlet{myred}{red!85!black}
\colorlet{myblue}{blue!80!black}
\colorlet{mycyan}{cyan!80!black}
\colorlet{mygreen}{green!70!black}
\colorlet{myorange}{orange!90!black!80}
\colorlet{mypurple}{red!50!blue!90!black!80}
\colorlet{mydarkred}{myred!80!black}
\colorlet{mydarkblue}{myblue!80!black}
\tikzstyle{xline}=[xcol,thick]
\tikzstyle{Tline}=[line width=0.6]
\tikzstyle{width}=[{Latex[length=5,width=3]}-{Latex[length=5,width=3]},thick]
\def\tick#1#2{\draw[thick] (#1)++(#2:0.12) --++ (#2-180:0.24)}
\def\N{100} % number of samples
\begin{document}
% POLYNOMIAL
% y = (x+1)*(x-1)^2
%   = x^3-x^2-x+1
\begin{tikzpicture}
  \message{^^JPolynomial}
  \def\a{(0.5*\xmax)} % root
  \def\A{(0.67*\ymax)} % amplitude
  \def\xmax{2.8}    % max x axis
  \def\ymax{1.7}    % max y axis
 
 
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