%This command provides the additional trigonometric functions
%displayed in the column three of the page 4
%
%The command has one parameter:
%        1) The width of the text
\newcommand\TFourTrigTwo[1]{%
\parbox[t]{#1}{%
   \deflength\TmpLengthA{3ex plus .5ex minus 1.5ex}
   \DisplaySpace{\TFourDisplaySpace}{\TFourDisplayShortSpace}
   %Since the width of the column is narrow, ragged right
   %looks better
   \raggedright

   \input{triangle.tex}
   \usebox\TriangleBox

   \TFourTitle{Law of cosines:}
   \begin{DisplayFormulae}{1}{0pt}{\TmpLengthA}{\BigChar}{\StyleWithoutNumber}
      \def\FirstPart{c^2 = \mbox{}}
      \FmPartA{\FirstPart a^2 + b^2 -}.
      \FmPartB{\FirstPart}{2ab \cos C}.
   \end{DisplayFormulae}

   \TFourTitle{Area:}
   \AdjustSpace{-2.5ex plus .5ex minus .5ex}
   \begin{DisplayFormulae}{1}{0pt}{1.1\TmpLengthA}{\BigChar}{\StyleWithoutNumber}
       \def\FirstPart{A}
       \FmPartA{\FirstPart = \tfrac{1}{2} h c = \tfrac{1}{2} a b \sin C}
       \FmPartB{\FirstPart}{= \tfrac{c^2 \sin A \sin B}{2 \sin C}}
   \end{DisplayFormulae}

   \TFourTitle{Heron's formula:}
   \begin{DisplayFormulae}{1}{0pt}{.9\TmpLengthA}{\BigChar}{\StyleWithoutNumber}
       \Fm{A = \sqrt{s \cdot s_a \cdot s_b \cdot s_c}}
       \Fm{s = \tfrac{1}{2} (a + b + c)}
       \Fm{s_a  = s - a}
       \Fm{s_b  = s - b}
       \Fm{s_c  = s - c}
   \end{DisplayFormulae}

   \TFourTitle{More identities:}
      \begin{DisplayFormulae}{1}{0pt}{\TmpLengthA}{\BigChar}{\StyleWithoutNumber}
         \def\FmSep{\unskip\text{,}}%Comma is the separator of equation
         \Fm{\sin \tfrac{x}{2} = \sqrt{\dfrac{1 - \cos x}{2}}}
         \Fm{\cos \tfrac{x}{2} = \sqrt{\dfrac{1 + \cos x}{2}}}
         \def\FirstPart{\tan \tfrac{x}{2}}%
         \FmPartA{\FirstPart = \sqrt{\dfrac{1 - \cos x}{1 + \cos x}}}
         \FmPartB{\FirstPart}{\!= \dfrac{1 - \cos x}{\sin x}}
         \FmPartB{\FirstPart}{\!= \dfrac{\sin x}{1 + \cos x}}
         \def\FirstPart{\cot \tfrac{x}{2}}
         \FmPartA{\FirstPart = \sqrt{\dfrac{1 + \cos x}{1 - \cos x}}}
         \FmPartB{\FirstPart}{\!=\dfrac{1 + \cos x}{\sin x}}
         \FmPartB{\FirstPart}{\!=\dfrac{\sin x}{1 - \cos x}}
         \Fm{\sin x = \dfrac{e^{ix} - e^{-ix}}{2 i}}
         \Fm{\cos x = \dfrac{e^{ix} + e^{-ix}}{2}}
         \def\FirstPart{\tan x} 
         \FmPartA{\FirstPart = -i \dfrac{e^{ix} - e^{-ix}}{e^{ix} + e^{-ix}}}
         \FmPartB{\FirstPart}{\!=-i \dfrac{e^{2ix} - 1}{e^{2ix} + 1}}
         \Fm{\sin x = \dfrac{\sinh i x}{i}}
         \Fm{\cos x = \cosh i x}
         \def\FmSep{\unskip\text{.}}
         \Fm{\tan x = \dfrac{\tanh i x}{i}}
   \end{DisplayFormulae}
   }%
}
