# drawing a polar type region and shading area using latex [closed]

I would like to draw the attached picture and insert it in a latex document. I was wondering if someone can help me?

• While you wait for an answer, consider going through your previous answers and accepting them, if appropriate. You can accept an answer by clicking on the check mark left of it. (The downvote does not come from me.) – user121799 Aug 17 '18 at 14:50

\documentclass[tikz,border=3.14mm]{standalone}
\makeatletter % https://tex.stackexchange.com/a/127045/121799
\makeatother

\usetikzlibrary{patterns,intersections,backgrounds}
\begin{document}
\begin{tikzpicture}
\draw[latex-latex] (0,5) node[left]{$y$} -- (0,0) coordinate(O) -- (8,0) node[below]{$x$};
\draw[save path=\pathA,name path=A](0,0) -- (50:4) coordinate[label=above:$A$](A)
to[out=50,in=130] ++(0.7,-0.5) coordinate (aux)
to[out=-50,in=90] ++(0.7,-0.5) coordinate[label=right:$B$] (B)
--cycle;
\begin{scope}
\clip [use path=\pathA];
\fill[pattern=north east lines] ([yshift=5pt]A) rectangle (B|-O);
\end{scope}
\draw[dashed] (A) -- (A-|O) coordinate[label=left:$E$] (E)
(B) -- (B|-O) coordinate[label=below:$C$] (C);
\draw[name path=BF,dashed] (B) -- (B-|O) coordinate[label=left:$F$] (F);
\draw[name path=AD,dashed](A) -- (A|-O) coordinate[label=below:$D$] (D);
\fill[name intersections={of=A and BF,by=H}] (H) coordinate[label=above left:$H$]
circle(1pt);
\fill[name intersections={of=A and AD,by={dummy,J}}] (J) coordinate[label=below right:$J$]
circle(1pt);
\fill (F-|D) coordinate[label=below left:$G$] (G) circle (1pt);
\draw[latex-] (aux) to[out=50,in=180] ++(0.5,0.5) node[right]{$r=f(\theta)$};
\begin{scope}[on background layer]
\clip (O) -- (B) -- ++(0,3cm) -| cycle;
\fill[pattern=north west lines,pattern color=red] [use path=\pathA];
\end{scope}
\begin{scope}[on background layer]
\clip (F) -- (B) |- ([yshift=1cm]E) -- cycle;
\fill[pattern=vertical lines,pattern color=blue] [use path=\pathA];
\end{scope}
\end{tikzpicture}

\begin{tikzpicture}
\draw[latex-latex] (0,5) node[left]{$y$} -- (0,0) coordinate(O) -- (8,0) node[below]{$x$};
\draw[save path=\pathA,name path=A](0,0) -- (50:4) coordinate[label=above:$A$](A)
to[out=50,in=130] ++(0.7,-0.5) coordinate (aux)
to[out=-50,in=90] ++(0.7,-0.5) coordinate[label=right:$B$] (B)
-- (B|-O)
--cycle;
\begin{scope}
\clip [use path=\pathA];
\fill[pattern=north east lines] ([yshift=5pt]A) rectangle (B|-O);
\end{scope}
\draw[dashed] (A) -- (A-|O) coordinate[label=left:$E$] (E)
(B) -- (B|-O) coordinate[label=below:$C$] (C);
\draw[name path=BF,dashed] (B) -- (B-|O) coordinate[label=left:$F$] (F);
\draw[name path=AD,dashed](A) -- (A|-O) coordinate[label=below:$D$] (D);
\fill[name intersections={of=A and BF,by=H}] (H) coordinate[label=above left:$H$]
circle(1pt);
\draw[name path=BO] (B) -- (O);
\fill[name intersections={of=BO and AD,by={G}}] (G) coordinate[label=below left:$G$]
circle(1pt);
\draw[latex-] (aux) to[out=50,in=180] ++(0.5,0.5) node[right]{$r=f(\theta)$};
\begin{scope}[on background layer]
\clip (O) -- (B) -- ++(0,3cm) -| cycle;
\fill[red,opacity=0.3] [use path=\pathA];
\end{scope}
\begin{scope}[on background layer]
\clip (F) -- (B) |- ([yshift=1cm]E) -- cycle;
\fill[blue,opacity=0.3] [use path=\pathA];
\end{scope}
\end{tikzpicture}

\begin{tikzpicture}
\draw[latex-latex] (0,5) node[left]{$y$} -- (0,0) coordinate(O) -- (8,0) node[below]{$x$};
\draw[save path=\pathA,name path=A](0,0) -- (50:4) coordinate[label=above:$A$](A)
to[out=50,in=130] ++(0.7,-0.5) coordinate (aux)
to[out=-50,in=90] ++(0.7,-0.5) coordinate[label=right:$B$] (B)
-- (B|-O)
--cycle;
\draw[dashed] (A) -- (A-|O) coordinate[label=left:$E$] (E)
(B) -- (B|-O) coordinate[label=below:$C$] (C);
\draw[name path=BF,dashed] (B) -- (B-|O) coordinate[label=left:$F$] (F);
\draw[name path=AD,dashed](A) -- (A|-O) coordinate[label=below:$D$] (D);
\fill[name intersections={of=A and BF,by=H}] (H) coordinate[label=above left:$H$]
circle(1pt);
\draw[name path=BO] (B) -- (O);
\fill[name intersections={of=BO and AD,by={G}}] (G) coordinate[label=below left:$G$]
circle(1pt);
\draw[latex-] (aux) to[out=50,in=180] ++(0.5,0.5) node[right]{$r=f(\theta)$};
%
\path (O-|H) coordinate[label=below:$M$](M)
(A-|H) coordinate[label=above:$N$](N);
\draw[dashed] (N) -- (M);
\begin{scope}[on background layer]
\fill[red,opacity=0.3] (E) -- (A) to[out=50,in=130]  (aux)
to[out=-50,in=90] (B) -- (F) -- cycle;
\end{scope}
\end{tikzpicture}
\end{document}


• Thanks for wonderful graphs! Also, What would be the code for indicating area of EABF and AOB? Thank you so much! – mathsolver Aug 17 '18 at 18:26
• @user2328489 Thanks for accepting an answer for the first time. Now there are three more to go. ;-) I made an update. I made an update with two different ways of indicating the areas. Please accept the other answers as well, at least those who someone else gave an answer. – user121799 Aug 17 '18 at 18:37
• I posted a new question from your graphs. How could we show the region enclosed by the vertices A E F B? – mathsolver Aug 17 '18 at 21:07
• @user2328489 I added this but will decouple now. Note that it is against the rules of this site to answer extra things that get added afterwards to an answer. You should simply ask a new question. It is free. And if you include a code of what you already tried (as opposed to a screen shot), people will be eager to help you. They will help you even more if you accept the answers to your previous questions. This is just 3 mouse clicks for you (your questions are listed under your profile). – user121799 Aug 17 '18 at 23:22
• marmot, thank you so much. Eventually, I could figure out your way of doing things. – mathsolver Aug 18 '18 at 0:53