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A free of charge answer with PSTricks. Compile it with xelatex for your convenience or with latex->dvips->ps2pdf for my convenience. Option 1 \documentclass[pstricks,border=12pt,12pt]{standalone} \usepackage{pst-eucl} \begin{document} \begin{pspicture}(-5,-5)(5,5) \psline(-5,0)(5,0) \psline(0,-5)(0,5) ...

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Try this quick solution: \documentclass[12pt,border=0.125cm]{standalone} \usepackage{tikz} \begin{document} \begin{tikzpicture}[line width=0.7pt,p/.style={circle,fill,inner sep=1.5pt}] \draw (1,0)node[yshift=-1cm]{$\mathcal{R}(A)$} -- (9,0)node[yshift=1cm,left]{$Ax_{1s}$} (5,4)--(5,-4) (1,-2)--(9,2); \draw [dashed](7,1)node[p]{}--node[right]{$r$} ...

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Also the final code looks like this, for someone to facilitate his work: \def\Sx{-2} \def\Sy{-3} \def\Sz{2} \pgfmathsetmacro\Sρ{"sqrt((\Sx)^(2)+(\Sy)^(2)+(\Sz)^(2))"} \pgfmathsetmacro\Sθ{ifthenelse(\Sx==0&&\Sy==0&&\Sz==0,0,"acos(\Sz/(sqrt((\Sx)^(2)+(\Sy)^(2)+(\Sz)^(2))))")} ...

2

The expression \pgfmathsetmacro\polar{ ifthenelse(\Sx=0 \AND \Sy=0 \AND \Sz=0, 0, acos(\Sz/(sqrt(\Sx^(2) + \Sy^(2) + \Sz^(2)))))} has several errors. The ifthenelse keyword implemented by pgf has a different syntax from the \ifthenelse macro from the ifthen package. You seem to be trying to mix the two, hence the issue. For the ifthenelse ...

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For the rotation of the labels, you can use visualization depends on = x \as \pgfplotspointx, every node near coord/.style={ rotate = \pgfplotspointx } This makes the value of the x coordinates available in a macro called \pgfplotspointx, which is then used for the rotation. To add the labels for the angle along the comb, you can use every node near ...

3

The arcsin function has a range from -pi/2 to pi/2 in radians or -90 to 90 in degrees. The later is used by the pgf package. That answers your first question. To compute the polar angle (here better: azimuth) for a cartesian point (x,y), you can use the following formula: The range of this polar angle is from -pi to pi or -180 degrees to 180 degrees. ...

4

By default, tikz uses centimeters (cm) as unit. You are using dimensions of the order of 200 (meaning 200cm) resulting in your image going beyond page and part of the image is not seen. Try setting [x=1mm,y=1mm], specifying all dimensions in mm and changing (unrelated) all tikzstyles (deprecated) to tikzset brings the image within the page. ...

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