Small-angle approximation

Small-angle approximation of sine, cosine and tangent, and their relative error.

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

Edit and compile if you like:

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% Author: Izaak Neutelings (June 2020)
\documentclass[border=3pt,tikz]{standalone}
\usepackage{amsmath} % for \text
\usepackage[outline]{contour} % glow around text
\usepackage{physics}
\usepackage{siunitx}
\usepackage{xcolor}
\usepackage{etoolbox} %ifthen
\usetikzlibrary{calc}
\usetikzlibrary{arrows,arrows.meta}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{angles,quotes} % for pic (angle labels)
%\usetikzlibrary{fadings}
\usepackage{etoolbox} % ifthen
\tikzset{>=latex} % for LaTeX arrow head
\contourlength{1.6pt}
\colorlet{myblue}{blue!60!black}
\colorlet{myred}{red!60!black}
\colorlet{mypurple}{red!50!blue!95!black!75}
\colorlet{mygreen}{green!60!black}
\tikzstyle{mydashed}=[black!70,dashed,thin]
\tikzstyle{mymeas}=[{Latex[length=3,width=2]}-{Latex[length=3,width=2]},thin]
\tikzstyle{mysmallarr}=[-{Latex[length=3,width=2]}]
\tikzset{
  declare function={reldiff(\x,\y) = (\x-\y)/abs(\y);}
}
\def\tick#1#2{\draw[thick] (#1) ++ (#2:0.1) --++ (#2-180:0.2)}
\begin{document}
% SIN - X - TAN
\def\A{2.0}
\def\k{0.45} % x -> theta
\def\xmax{4.2}
\def\ymax{\A}
\def\N{7}
 
 
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