\documentclass[10pt,a4paper]{article}

% Packages
\usepackage{fancyhdr}           % For header and footer
\usepackage{multicol}           % Allows multicols in tables
\usepackage{tabularx}           % Intelligent column widths
\usepackage{tabulary}           % Used in header and footer
\usepackage{hhline}             % Border under tables
\usepackage{graphicx}           % For images
\usepackage{xcolor}             % For hex colours
%\usepackage[utf8x]{inputenc}    % For unicode character support
\usepackage[T1]{fontenc}        % Without this we get weird character replacements
\usepackage{colortbl}           % For coloured tables
\usepackage{setspace}           % For line height
\usepackage{lastpage}           % Needed for total page number
\usepackage{seqsplit}           % Splits long words.
%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
\usepackage[normalem]{ulem}     % For underlining links
% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
\usepackage{MnSymbol}           % Symbols
\usepackage{wasysym}            % Symbols
%\usepackage[english,german,french,spanish,italian]{babel}              % Languages

% Document Info
\author{CROSSANT (CROSSANT)}
\pdfinfo{
  /Title (integral-trigonometry.pdf)
  /Creator (Cheatography)
  /Author (CROSSANT (CROSSANT))
  /Subject (Integral Trigonometry Cheat Sheet)
}

% Lengths and widths
\addtolength{\textwidth}{6cm}
\addtolength{\textheight}{-1cm}
\addtolength{\hoffset}{-3cm}
\addtolength{\voffset}{-2cm}
\setlength{\tabcolsep}{0.2cm} % Space between columns
\setlength{\headsep}{-12pt} % Reduce space between header and content
\setlength{\headheight}{85pt} % If less, LaTeX automatically increases it
\renewcommand{\footrulewidth}{0pt} % Remove footer line
\renewcommand{\headrulewidth}{0pt} % Remove header line
\renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit
% This two commands together give roughly
% the right line height in the tables
\renewcommand{\arraystretch}{1.3}
\onehalfspacing

% Commands
\newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour
\newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols
\newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns
\newcommand{\tn}{\tabularnewline} % Required as custom column type in use

% Font and Colours
\definecolor{HeadBackground}{HTML}{333333}
\definecolor{FootBackground}{HTML}{666666}
\definecolor{TextColor}{HTML}{333333}
\definecolor{DarkBackground}{HTML}{C27A0E}
\definecolor{LightBackground}{HTML}{FBF6EF}
\renewcommand{\familydefault}{\sfdefault}
\color{TextColor}

% Header and Footer
\pagestyle{fancy}
\fancyhead{} % Set header to blank
\fancyfoot{} % Set footer to blank
\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
    }
\end{tabulary}
\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Integral Trigonometry Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{CROSSANT (CROSSANT)} via \textcolor{DarkBackground}{\uline{cheatography.com/186482/cs/38992/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}CROSSANT (CROSSANT) \\
  \uline{cheatography.com/crossant} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 28th May, 2023.\\
   Updated 7th October, 2024.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
  \SetRowColor{white}
  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

% Set font size to small. Switch to any value
% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{3.08574 cm} x{1.89126 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Basic Trigonometric Integrals}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{∫sin(x)dx}} & {\bf{-cos(x)+C}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
{\bf{∫cos(x)dx}} & {\bf{sin(x)+C}} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
{\bf{∫sec\textasciicircum{}2\textasciicircum{}(x)dx}} & {\bf{tan(x)+C}} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
{\bf{∫sec(x)tan(x)dx}} & {\bf{sec(x)+C}} \tn 
% Row Count 4 (+ 1)
% Row 4
\SetRowColor{LightBackground}
∫csc\textasciicircum{}2\textasciicircum{}(x)dx & -cot(x)+C \tn 
% Row Count 5 (+ 1)
% Row 5
\SetRowColor{white}
∫csc(x)cot(x)dx & -csc(x)+C \tn 
% Row Count 6 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.59264 cm} x{3.38436 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Common Trigonometric Integrals}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{∫sin(2x)dx}} & {\bf{-$\frac{1}{2}$cos(2x)+C}} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
{\bf{∫cos(2x)dx}} & {\bf{$\frac{1}{2}$sin(2x)+C}} = sin(x)cos(x)+C \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
∫tan(x)dx & ln|sec(x)|+C \tn 
% Row Count 5 (+ 1)
% Row 3
\SetRowColor{white}
∫sec(x)dx & ln|sec(x)+tan(x)|+C \tn 
% Row Count 6 (+ 1)
% Row 4
\SetRowColor{LightBackground}
∫sec\textasciicircum{}3\textasciicircum{}(x)dx & $\frac{1}{2}$(sec(x)tan(x)+ln|sec(x)+tan(x)|)+C \tn 
% Row Count 8 (+ 2)
% Row 5
\SetRowColor{white}
∫csc(x)dx & -ln|csc(x)+cot(x)|+C \tn 
% Row Count 10 (+ 2)
% Row 6
\SetRowColor{LightBackground}
∫csc\textasciicircum{}3\textasciicircum{}(x)dx & -$\frac{1}{2}$(csc(x)cot(x)+ln|csc(x)+cot(x)|)+C \tn 
% Row Count 14 (+ 4)
% Row 7
\SetRowColor{white}
{\bf{∫1/(1+x\textasciicircum{}2\textasciicircum{})dx}} & {\bf{arctan(x)+C}} \tn 
% Row Count 16 (+ 2)
% Row 8
\SetRowColor{LightBackground}
∫1/(a\textasciicircum{}2\textasciicircum{}+x\textasciicircum{}2\textasciicircum{})dx & (1/a)arctan(x/a)+C \tn 
% Row Count 18 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.59264 cm} x{3.38436 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Secant and Cosecant Integrals}}  \tn
% Row 0
\SetRowColor{LightBackground}
Secant Integral 1 & ∫sec(x)dx = ln|sec(x)+tan(x)|+C \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Secant Integral 2 & ∫sec(x)dx = -ln|sec(x)-tan(x)|+C \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Secant Integral 3 & ∫sec(x)dx = $\frac{1}{2}$ln|(sin(x)+1)/(sin(x)-1)|+C \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
Secant Integral 4 & ∫sec(x)dx = ln|tan(x/2+π/4)|+C \tn 
% Row Count 8 (+ 2)
% Row 4
\SetRowColor{LightBackground}
Cosecant Integral 1 & ∫csc(x)dx = ln|csc(x)-cot(x)|+C \tn 
% Row Count 10 (+ 2)
% Row 5
\SetRowColor{white}
Cosecant Integral 2 & ∫csc(x)dx = -ln|csc(x)+cot(x)|+C \tn 
% Row Count 12 (+ 2)
% Row 6
\SetRowColor{LightBackground}
Cosecant Integral 3 & ∫csc(x)dx = $\frac{1}{2}$ln|(cos(x)-1)/(cos(x)+1)|+C \tn 
% Row Count 14 (+ 2)
% Row 7
\SetRowColor{white}
Cosecant Integral 4 & ∫csc(x)dx = ln|tan(x/2)|+C \tn 
% Row Count 16 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Sine and Cosine Unit Circle}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/crossant_1685307647_Sine and Cosine Unit Circle.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Powers of Trigonometric Functions}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{\seqsplit{https://cheatography.com/crossant/cheat-sheets/integral-cases-for-trigonometric-powers/}% Row Count 2 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.43873 cm} x{2.53827 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Quotient and Reciprocal Identities}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Tangent Quotient}} & {\bf{tan(x)=sin(x)/cos(x)}} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
{\bf{Cotangent Quotient}} & {\bf{cot(x)=cos(x)/sin(x)}} \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{} \tn 
% Row Count 4 (+ 0)
% Row 3
\SetRowColor{white}
Sine Reciprocal & sin(x)=1/csc(x) \tn 
% Row Count 5 (+ 1)
% Row 4
\SetRowColor{LightBackground}
Cosine Reciprocal & cos(x)=1/sec(x) \tn 
% Row Count 6 (+ 1)
% Row 5
\SetRowColor{white}
Tangent Reciprocal & tan(x)=1/cot(x) \tn 
% Row Count 7 (+ 1)
% Row 6
\SetRowColor{LightBackground}
{\bf{Cosecant Reciprocal}} & {\bf{csc(x)=1/sin(x)}} \tn 
% Row Count 9 (+ 2)
% Row 7
\SetRowColor{white}
{\bf{Secant Reciprocal}} & {\bf{sec(x)=1/cos(x)}} \tn 
% Row Count 11 (+ 2)
% Row 8
\SetRowColor{LightBackground}
Cotangent Reciprocal & cot(x)=1/tan(x) \tn 
% Row Count 13 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.73735 cm} x{2.23965 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Pythagorean Identities}}  \tn
% Row 0
\SetRowColor{LightBackground}
Sine-Cosine Pythagorean & {\bf{sin\textasciicircum{}2\textasciicircum{}(x)+cos\textasciicircum{}2\textasciicircum{}(x)=1}} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Sine Pythagorean & {\bf{sin\textasciicircum{}2\textasciicircum{}(x)=1-cos\textasciicircum{}2\textasciicircum{}(x)}} \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Cosine Pythagorean & {\bf{cos\textasciicircum{}2\textasciicircum{}(x)=1-sin\textasciicircum{}2\textasciicircum{}(x)}} \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
Secant Pythagorean & {\bf{tan\textasciicircum{}2\textasciicircum{}(x)+1=sec\textasciicircum{}2\textasciicircum{}(x)}} \tn 
% Row Count 8 (+ 2)
% Row 4
\SetRowColor{LightBackground}
Tangent Pythagorean & {\bf{tan\textasciicircum{}2\textasciicircum{}(x)=sec\textasciicircum{}2\textasciicircum{}(x)-1}} \tn 
% Row Count 10 (+ 2)
% Row 5
\SetRowColor{white}
Secant-Tangent Pythagorean & sec\textasciicircum{}2\textasciicircum{}(x)-tan\textasciicircum{}2\textasciicircum{}(x)=1 \tn 
% Row Count 12 (+ 2)
% Row 6
\SetRowColor{LightBackground}
Cosecant Pythagorean & 1+cot\textasciicircum{}2\textasciicircum{}(x)=csc\textasciicircum{}2\textasciicircum{}(x) \tn 
% Row Count 14 (+ 2)
% Row 7
\SetRowColor{white}
Cotangent Pythagorean & cot\textasciicircum{}2\textasciicircum{}(x)=csc\textasciicircum{}2\textasciicircum{}(x)-1 \tn 
% Row Count 16 (+ 2)
% Row 8
\SetRowColor{LightBackground}
Cosecant-Cotangent Pythagorean & csc\textasciicircum{}2\textasciicircum{}(x)-cot\textasciicircum{}2\textasciicircum{}(x)=1 \tn 
% Row Count 18 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{The last two triplets of Pythagorean identities are obtained by dividing all the terms of the original identity by sin$^{\textrm{2}}$(x) or cos$^{\textrm{2}}$(x)}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Sum and Difference Identities}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{sin(x+y)=sin(x)cos(y) + cos(x)sin(y)} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{sin(x-y)=sin(x)cos(y) - cos(x)sin(y)} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{cos(x+y)=cos(x)cos(y) - sin(x)sin(y)} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{cos(x-y)=cos(x)cos(y) + sin(x)sin(y)} \tn 
% Row Count 4 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Right-Triangle Trigonometric Relations}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/crossant_1685307563_Labeled Right Triangle.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.05271 cm} x{1.46464 cm} x{2.05965 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{Trigonometric Substitutions}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{a\textasciicircum{}2\textasciicircum{}-x\textasciicircum{}2\textasciicircum{}}} & {\bf{Let x=asin(θ)}} & {\bf{dx=acos(θ)dθ}} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
{\bf{x\textasciicircum{}2\textasciicircum{}-a\textasciicircum{}2\textasciicircum{}}} & {\bf{Let x=asec(θ)}} & {\bf{dx=asec(θ)tan(θ)dθ}} \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
{\bf{x\textasciicircum{}2\textasciicircum{}+a\textasciicircum{}2\textasciicircum{}}} & {\bf{Let x=atan(θ)}} & {\bf{dx=asec\textasciicircum{}2\textasciicircum{}(θ)dθ}} \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
a\textasciicircum{}2\textasciicircum{}-b\textasciicircum{}2\textasciicircum{}x\textasciicircum{}2\textasciicircum{} & Let \seqsplit{x=(a/b)sin(θ)} & \seqsplit{dx=(a/b)cos(θ)dθ} \tn 
% Row Count 8 (+ 2)
% Row 4
\SetRowColor{LightBackground}
b\textasciicircum{}2\textasciicircum{}x\textasciicircum{}2\textasciicircum{}-a\textasciicircum{}2\textasciicircum{} & Let \seqsplit{x=(a/b)sec(θ)} & \seqsplit{dx=(a/b)sec(θ)tan(θ)dθ} \tn 
% Row Count 10 (+ 2)
% Row 5
\SetRowColor{white}
b\textasciicircum{}2\textasciicircum{}x\textasciicircum{}2\textasciicircum{}+a\textasciicircum{}2\textasciicircum{} & Let \seqsplit{x=(a/b)tan(θ)} & dx=(a/b)sec\textasciicircum{}2\textasciicircum{}(θ)dθ \tn 
% Row Count 12 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\SetRowColor{LightBackground}
\mymulticolumn{3}{x{5.377cm}}{Trigonometric substitutions are typically used under radicals, however, they are not required to be \newline  \newline For definite integrals, you will need to set x equal to its respective bounds, and solve for θ in order to properly change the bounds of integration with respect to θ}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.38896 cm} x{2.58804 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Half-Angle and Double-Angle Identities}}  \tn
% Row 0
\SetRowColor{LightBackground}
Sine Half-Angle & sin(x/2)={\bf{√}}($\frac{1}{2}$(1-cos(x))) \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Cosine Half-Angle & cos(x/2)={\bf{√}}($\frac{1}{2}$(1+cos(x))) \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
{\bf{Sine Power-Reducing}} & {\bf{sin\textasciicircum{}2\textasciicircum{}(x)=$\frac{1}{2}$(1-cos(2x))}} \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
{\bf{Cosine Power-Reducing}} & {\bf{cos\textasciicircum{}2\textasciicircum{}(x)=$\frac{1}{2}$(1+cos(2x))}} \tn 
% Row Count 8 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{} \tn 
% Row Count 8 (+ 0)
% Row 5
\SetRowColor{white}
{\bf{Sine Double-Angle}} & {\bf{sin(2x)=2sin(x)cos(x)}} \tn 
% Row Count 10 (+ 2)
% Row 6
\SetRowColor{LightBackground}
{\bf{Cosine Double-Angle 1}} & {\bf{cos(2x)=cos\textasciicircum{}2\textasciicircum{}(x)-sin\textasciicircum{}2\textasciicircum{}(x)}} \tn 
% Row Count 12 (+ 2)
% Row 7
\SetRowColor{white}
Cosine Double-Angle 2 & cos(2x)=2cos\textasciicircum{}2\textasciicircum{}(x)-1 \tn 
% Row Count 14 (+ 2)
% Row 8
\SetRowColor{LightBackground}
Cosine Double-Angle 3 & cos(2x)=1-2sin\textasciicircum{}2\textasciicircum{}(x) \tn 
% Row Count 16 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{Sine Power-Reducing and Cosine Power-Reducing identities are variations of the Half-Angle identities}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Tangent Unit Circle}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/crossant_1685308007_Tangent Unit Circle.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}