[Tex/LaTex] Drawing and labeling angles in an axis environment

pgfplotstikz-pgf

I am curious about the misinterpretation of TikZ commands to draw and label an angle in an axis environment. If, in the following code, I have $\theta$ drawn using the commands,

\draw[draw=blue] (A) ++(120:4mm) arc (120:0:4mm);
\coordinate (label_for_theta) at (60:5.5mm);
\node[font=\footnotesize] at (label_for_theta){$\theta$};

the angle and label are displayed as expected. I have, though,

\draw[draw=blue] (A) ++(120:0.4) arc (120:0:0.4);
\coordinate (label_for_theta) at (60:0.55);
\node[font=\footnotesize] at (label_for_theta){$\theta$};

and a mess is displayed. I understand that using the axis environment is superfluous – I am using it just to draw the axes. As I said, I am curious. (I know that I could use tkz-euclice. I am using this as an opportunity to get familiar with TikZ. I would prefer to avoid using this package, anyway.)

By the way, I typeset the vertex A properly with \node at (0.25,-0.25){$A$};, without units, and I typeset the vertex B properly with \node at (3.5,-2.5mm){$B$};, with units. I was told that specifying coordinates with dimensions within an axis environment would be misinterpreted.

\documentclass{amsart}
\usepackage{amsmath}
\usepackage{amsfonts}

\usepackage{tikz}
\usetikzlibrary{calc,angles,positioning,intersections,quotes,decorations.markings,backgrounds,patterns}

\usepackage{pgfplots}
\pgfplotsset{compat=1.11}


\begin{document}


\begin{tikzpicture}
\begin{axis}[width=5in,axis equal image,
    axis lines=middle,
    xmin=-5,xmax=5,
    ymin=-1.5,ymax=5,
    restrict y to domain=-1.5:5,
    xtick={\empty},ytick={\empty},
    axis line style={latex-latex},
    xlabel=$x$,ylabel=$y$,
    xlabel style={at={(ticklabel* cs:1)},anchor=north west},
    ylabel style={at={(ticklabel* cs:1)},anchor=south west}
]

%A triangle is drawn on the Cartesian plane. One side of the triangle is along
%the positive x-axis, and another side of the triangle is drawn in Quadrant II.
\coordinate (A) at (0,0);
\coordinate (B) at (3.5,0);
\coordinate (C) at ({5*cos(120)},{5*sin(120)});
\draw (A) -- (B) -- (C) -- cycle;

%The labels for A and B are typeset.
\node at (0.25,-0.25){$A$};
\node at (3.5,-2.5mm){$B$};
%The label for C is typeset.
\coordinate (label_C_left) at ($(C)!-4mm!(B)$);
\coordinate (label_C_right) at ($(C)!-4mm!(A)$);
\coordinate (label_C) at ($(label_C_left)!0.5!(label_C_right)$);
\node[blue] at ($(C)!2.5mm!(label_C)$){$C$};


%Angles are drawn for $\theta$ and its supplement.
\draw[draw=blue] (A) ++(120:0.4) arc (120:0:0.4);
\coordinate (label_for_theta) at (60:0.55);
\node[font=\footnotesize] at (label_for_theta){$\theta$};
\draw[draw=blue,dash dot] (A) ++(180:0.6) arc (180:120:0.6);
\coordinate (label_for_supplement_to_theta) at (150:0.75);
\node[font=\footnotesize] at (label_for_supplement_to_theta){$\pi - \theta$};


%A right-angle mark is drawn.
\coordinate (U) at ($(-2.5,0)!3mm!45:(A)$);
\draw[dash dot] (U) -- ($(-2.5,0)!(U)!(A)$);
\draw[dash dot] (U) -- ($(-2.5,0)!(U)!(C)$);


\draw[dashed] (C) -- (-2.5,0);

%Braces indicating the distances that C is from the axes are typeset. To give
%them the appearance of being typeset over the axes, they are first typeset
%in white with a line width of 2pt, which is 10 times the thickness of the
%brace that is actually typeset.
\draw[draw=white,line width=4pt,decorate,decoration={brace,raise=5pt,amplitude=5pt}] (-2.5,0) -- (C);
\draw[decorate,decoration={brace,raise=5pt,amplitude=5pt}] (-2.5,0) -- (C);
\draw[draw=white,line width=4pt,decorate,decoration={brace,raise=5pt,amplitude=5pt,mirror}] (-2.5,0) -- (A);
\draw[decorate,decoration={brace,raise=5pt,amplitude=5pt,mirror}] (-2.5,0) -- (A);


\coordinate (label_for_5_sin_theta) at ($({5*cos(120)},{2.5*sin(120)}) + (-2.5mm-10pt,0pt)$);
\node[anchor=east] at (label_for_5_sin_theta){$r\sin\theta$};
\coordinate (label_for_5_cos_theta) at (-1.25,-2.5mm-10pt);
\node at (label_for_5_cos_theta){$r\cos\theta$};

\end{axis}
\end{tikzpicture}
\end{document}

Best Answer

If you only want to use the axis environment to draw the axis, then don't try to do anything else with it. Note: the scope is used to shift the origin.

I also simplified your angle labels. Later I came back and simplified all of the labels.

\documentclass{amsart}
\usepackage{amsmath}
\usepackage{amsfonts}

\usepackage{tikz}
\usetikzlibrary{calc,angles,positioning,intersections,quotes,decorations.markings,backgrounds,patterns}

\usepackage{pgfplots}
\pgfplotsset{compat=1.11}


\begin{document}


\begin{tikzpicture}
\begin{axis}[width=5in,axis equal image,
    axis lines=middle,
    xmin=-5,xmax=5,
    ymin=-1.5,ymax=5,
    restrict y to domain=-1.5:5,
    xtick={\empty},ytick={\empty},
    axis line style={latex-latex},
    xlabel=$x$,ylabel=$y$,
    xlabel style={at={(ticklabel* cs:1)},anchor=north west},
    ylabel style={at={(ticklabel* cs:1)},anchor=south west}
]
\coordinate (origin) at (0,0);
\end{axis}
\begin{scope}[shift={(origin)}]
%A triangle is drawn on the Cartesian plane. One side of the triangle is along
%the positive x-axis, and another side of the triangle is drawn in Quadrant II.
\coordinate (A) at (0,0);
\coordinate (B) at (3.5,0);
\coordinate (C) at ({5*cos(120)},{5*sin(120)});
\draw (A) -- (B) -- (C) -- cycle;

\coordinate (D) at (A-|C);% horizontal to (A), vertical to (C)

%The labels for A and B are typeset.
\node[below right] at (A){$A$};
\node[below] at (B){$B$};
%The label for C is typeset.
\node[blue,above left] at (C) {$C$};


%Angles are drawn for $\theta$ and its supplement.
\draw[draw=blue] (A) ++(120:0.4) arc (120:0:0.4)
  node[midway,above right,inner sep=2pt,font={\footnotesize}]{$\theta$};
\draw[draw=blue,dash dot] (A) ++(180:0.6) arc (180:120:0.6)
  node[midway,left,inner sep=2pt,font={\footnotesize}]{$\pi - \theta$};

%A right-angle mark is drawn.
\draw[dash dot] (D) +(0,3mm) -- +(3mm,3mm) -- +(3mm,0);

\draw[dashed] (C) -- (D);

%Braces indicating the distances that C is from the axes are typeset. To give
%them the appearance of being typeset over the axes, they are first typeset
%in white with a line width of 2pt, which is 10 times the thickness of the
%brace that is actually typeset.
\draw[draw=white,line width=4pt,decorate,decoration={brace,raise=.5em,amplitude=.5em}] (D) -- (C);
\draw[decorate,decoration={brace,raise=.5em,amplitude=.5em}] (D) -- (C)
  node[midway,left=1em] {$r\sin\theta$};;
\draw[draw=white,line width=4pt,decorate,decoration={brace,raise=1ex,amplitude=1ex,mirror}] (D) -- (A);
\draw[decorate,decoration={brace,raise=1ex,amplitude=1ex,mirror}] (D) -- (A)
  node[midway,below=2ex] {$r\cos\theta$};
\end{scope}
\end{tikzpicture}
\end{document}

Related Solutions

[Tex/LaTex] Rotate a node but not its content: the case of the ellipse decoration

The source of the difficulty is that ellipses are constructed in a particular way in TikZ. They are paths that start from the x-axis and proceed counter-clockwise around their centre. The vast majority of the time, the exact parametrisation doesn't matter. You appear to have found the one situation where it does!

In the actual question, you only want to be able to mirror the ellipse, and so draw it starting from the negative x-axis (the title of the question suggests a more flexible approach). That's actually not too hard since we can exploit the symmetry of the ellipse. The key is to provide it with a negative x-radius, since then it will start from the negative x-axis (and proceed clockwise, but we could correct for that by negating the y-radius as well). To do this, we interrupt the call from the node shape to the drawing command and flip the sign of the x-radius. The simplest way to do this is to redefine the \pgfpathellipse macro to do the negation and then call the original macro. The following code does this.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations,shapes,decorations.markings}
\makeatletter
\let\origpgfpathellipse=\pgfpathellipse
\def\revpgfpathellipse#1#2#3{%
  #2%
  \pgf@xa=-\pgf@x
  \origpgfpathellipse{#1}{\pgfqpoint{\pgf@xa}{0pt}}{#3}}
\makeatother

\tikzset{
  reversed ellipse/.style={
    ellipse,
    reverse the ellipse%
  },
  reverse the ellipse/.code={
    \let\pgfpathellipse=\revpgfpathellipse
  }
}
\begin{document}
\begin{tikzpicture}
\node[ellipse,
  draw,
  postaction={
    decorate,
    decoration={
      markings,
      mark=at position 1 with {
        \arrow[line width=5pt,blue]{>}
      }
    }
  }
] at (0,0) {hello world};

\node[reversed ellipse,
  draw,
  postaction={
    decorate,
    decoration={
      markings,
      mark=at position 1 with {
        \arrow[line width=5pt,blue]{>}
      }
    }
  }
] at (0,-2) {hello world};
\end{tikzpicture}

\end{document}

Here's the result:

rotated ellipse

(the arrow got clipped, but you can see where it lies)

[Tex/LaTex] Drawing and labeling asymptotes

You can use a node to put x=1 and y=1. Further, to draw a horizontal line at y=1, you can use \addplot: like

\addplot[samples=200,dashed,latex-latex,domain=-17:17] {1}node[above,pos=0]{$y=1$};

Full code:

\documentclass[10pt]{amsart}
%\usepackage{tikz}      %% These are all not needed
%\usetikzlibrary{calc,angles,positioning,intersections,quotes,decorations.markings}
%\usepackage{tkz-euclide}
%\usetkzobj{all}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}

%\usepackage{amsmath}
%\usepackage{amsfonts}
%\usepackage{amssymb}
%\usepackage{amsthm}

\begin{document}

\begin{tikzpicture}
\begin{axis}[width=4in,axis equal image,
    axis lines=middle,
    xmin=-15,xmax=15,
    xlabel=$x$,ylabel=$y$,
    ymin=-10,ymax=10,
    restrict y to domain=-12:12,
    enlargelimits={abs=1cm},
    axis line style={latex-latex},
    ticklabel style={font=\tiny,fill=white},
    xtick={-3},
    every axis y label/.style=
         {at={(ticklabel cs:1.02,-12pt)},rotate=0,anchor=west},
    every axis x label/.style={
         at={(xticklabel cs:1.02,-8pt)},anchor=south},
]
/pgfplots/xlabel shift={10pt};
\addplot[samples=250,domain=-15:15] {(x+2)/(x-1)};
\draw[dashed,shorten <=2ex, shorten >=2ex,latex-latex] ({{1,0}}|-{{axis description cs:1,1}}) -- ({{1,0}}|-{{axis description cs:1,0}})node[right,pos=0.95]{$x=1$};
\draw [fill=white] (-3,0.25) circle [radius=1.5pt] node[left]{};
\addplot[samples=200,dashed,latex-latex,domain=-17:17] {1}node[above,pos=0]{$y=1$};
\end{axis}
\end{tikzpicture}
\vskip0.25in


\begin{tikzpicture}
\begin{axis}[width=4in,axis equal image,
    axis lines=middle,
    xmin=-15,xmax=15,
    xlabel=$x$,ylabel=$y$,
    ymin=-10,ymax=10,
    restrict y to domain=-12:12,
    enlargelimits={abs=1cm},
    axis line style={latex-latex},
    ticklabel style={font=\tiny,fill=white},
    xtick={-1},ytick=\empty,
    every axis y label/.style=
         {at={(ticklabel cs:1.02,0pt)},rotate=0,},
    every axis x label/.style={
         at={(xticklabel cs:1.02,-8pt)},anchor=south},
]
/pgfplots/xlabel shift={10pt};
\addplot[samples=251,domain=-14:16] {(x+1)/(x-1)};
\draw[dashed,shorten <=2ex, shorten >=2ex,latex-latex] ({{1,0}}|-{{axis description cs:1,1}}) -- ({{1,0}}|-{{axis description cs:1,0}})node[right,pos=0.95]{$x=1$};
\addplot[samples=200,dashed,latex-latex,domain=-17:17] {1}node[above,pos=0]{$y=1$};

\end{axis}
\end{tikzpicture}

\end{document}

enter image description here

Best Answer

Related Solutions

[Tex/LaTex] Rotate a node but not its content: the case of the ellipse decoration

[Tex/LaTex] Drawing and labeling asymptotes

Related Question