Polar coordinates & radians

Definition of polar coordinates, unit vectors, angles, line segments and radians.
For more figures of coordinate system, have a look at the “coordinates” tag.

Definition of polar coordinates and unit vectors on a circle with radius r:

Definition of the radial length of an angle subtended by a circle segment:

Summary of important angles and their radians on the unit circle:

Edit and compile if you like:

% Author: Izaak Neutelings (September 2020)
\documentclass[border=3pt,tikz]{standalone}
\usepackage{amsmath}
\usepackage{tikz}
\usepackage{physics}
\usepackage{siunitx}
\usepackage[outline]{contour} % glow around text
\usetikzlibrary{angles,quotes} % for pic
\contourlength{1.3pt}
\tikzset{>=latex} % for LaTeX arrow head
\usepackage{xcolor}
\colorlet{veccol}{green!70!black}
\colorlet{vcol}{green!70!black}
\colorlet{xcol}{blue!85!black}
\colorlet{projcol}{xcol!60}
\colorlet{unitcol}{xcol!60!black!85}
\colorlet{unitcol2}{vcol!60!black!85}
\colorlet{myblue}{blue!70!black}
\colorlet{myred}{red!70!black}
\tikzstyle{vector}=[->,very thick,xcol]
\tikzstyle{mydashed}=[dash pattern=on 2pt off 2pt]
\def\tick#1#2{\draw[thick] (#1) ++ (#2:0.1) --++ (#2-180:0.2)} %0.03*\xmax
\begin{document}
% CIRCLE polar coordinates + vector
\def\xmax{2.0}
\def\ul{0.6}
\def\R{1.7}
\begin{tikzpicture}
\def\ang{43}
\coordinate (O) at (0,0);
\coordinate (X) at (\xmax,0);
\coordinate (R) at (\ang:\R);
\draw[->,line width=0.9] (-\xmax,0) -- (1.08*\xmax,0) node[right] {$x$};
\draw[->,line width=0.9] (0,-\xmax) -- (0,1.08*\xmax) node[left] {$y$};
\node[fill=black,circle,inner sep=0.9] (R') at (R) {};
\node[above right] at (R) {$(x,y)=(r;\theta)$};
 
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Click to download: circle.texcircle.pdf
Open in Overleaf: circle.tex

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