Directional Angles

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\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{math}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{0.125pt}
%
% File name: directional-angles.tex
% Description: 
% The directional angles of a vector are geometrically represented.
% 
% Date of creation: July, 25th, 2021.
% Date of last modification: October, 9th, 2022.
% Author: Efra�n Soto Apolinar.
% https://www.aprendematematicas.org.mx/author/efrain-soto-apolinar/instructing-courses/
% Source: page 11 of the 
% Glosario Ilustrado de Matem\'aticas Escolares.
% https://tinyurl.com/5udm2ufy
%
% Terms of use:
% According to TikZ.net
% https://creativecommons.org/licenses/by-nc-sa/4.0/
% Your commitment to the terms of use is greatly appreciated.
%
\begin{document}
    \tdplotsetmaincoords{80}{120}
    %
    \begin{tikzpicture}[tdplot_main_coords,scale=0.75] 
        % Indicate the components of the vector in rectangular coordinates
        \pgfmathsetmacro{\ux}{4}
        \pgfmathsetmacro{\uy}{4}
        \pgfmathsetmacro{\uz}{3}
        % Length of each axis
        \pgfmathsetmacro{\ejex}{\ux+0.5}
        \pgfmathsetmacro{\ejey}{\uy+0.5}
        \pgfmathsetmacro{\ejez}{\uz+0.5}
        \pgfmathsetmacro{\umag}{sqrt(\ux*\ux+\uy*\uy+\uz*\uz)} % Magnitude of vector $\vec{u}$
        % Compute the angle $\theta$
        \pgfmathsetmacro{\angthetax}{pi*atan(\uy/\ux)/180}
        \pgfmathsetmacro{\angthetay}{pi*atan(\ux/\uz)/180}
 
 
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