Answer by hpesoj626 for how can I fix my tikz circle to do what I want

Explanation

Use a polar coordinate instead. Since (3,3) makes an angle of 45 degrees with the positive part of the x-axis, and you have used 2.5 cm as your radius, you can specify the coordinate as (45:2.5cm), which implicitly means (canvas polar cs:angle=45,radius=2.5cm). You can see some more explanations in the pgf manual, page 125 in version 2.10.

Code

%\documentclass[paper=a4, fontsize=12pt]{scrartcl} \documentclass[preview,border=5]{standalone}\usepackage[T1]{fontenc} \usepackage{amsmath,amsfonts,amsthm} % Maths  \usepackage{graphicx} \usepackage{float}\usepackage{tikz}\usetikzlibrary{arrows,%                plotmarks}\begin{document} \begin{figure}[H] \centering   \begin{tikzpicture}    % Axis    \draw[thick,->,black] (-3,0)--(3,0) node[below] {$k_x$}; % x axis    \draw[thick,->,black] (0,-3)--(0,3) node[left] {$k_y$}; % y axis    \draw[black,thick] (0,0) circle (2.5cm);    \draw[ultra thick,blue,dashed=on 2pt off 3pt] (0,0) -- (45:2.5cm); % Use the polar coordinate (<angle>:<length>) instead   \end{tikzpicture}\end{figure}\end{document}

Output

Edit

I didn't see your second concern. Although I should advise you to limit your questions in one post in the future. See the modified code below. Some explanations:

• \pgflinewidth takes the value of line width key which is given here the value of 0.5pt.
• I have added fill=white to the nodes of your axis labels to distinguish them from the dotted lines and added some distance in order to not cover the arrows.

%\documentclass[paper=a4, fontsize=12pt]{scrartcl} \documentclass[preview,border=5]{standalone}\usepackage[T1]{fontenc} \usepackage{amsmath,amsfonts,amsthm} % Maths  \usepackage{graphicx} \usepackage{float}\usepackage{tikz}\usetikzlibrary{arrows,%                plotmarks,patterns}\begin{document} \begin{figure}[H] \centering   \begin{tikzpicture}   \draw [line width=0.5pt, line cap=round, dash pattern=on 0pt off 2\pgflinewidth] (-3,-3) grid (3,3);    % Axis    \draw[thick,->,black] (-3,0)--(3,0) node[below=1.75pt, fill=white] {$k_x$}; % x axis    \draw[thick,->,black] (0,-3)--(0,3) node[left=1.75pt, fill=white] {$k_y$}; % y axis    \draw[black,thick] (0,0) circle (2.5cm);    \draw[ultra thick,blue,dashed=on 2pt off 3pt] (0,0) -- (canvas polar cs:angle=45,radius=2.5cm);   \end{tikzpicture}\end{figure}\end{document}

Reference

See Dotted lines in TikZ with round dots for the different approaches for producing the dotted lines in tikz.