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) {$(x,y)=(r;\theta)$};
Click to download: circle.tex • circle.pdf
Open in Overleaf: circle.tex