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Diffstat (limited to 'info/mathtrip/src/hyper.tex')
-rw-r--r-- | info/mathtrip/src/hyper.tex | 54 |
1 files changed, 54 insertions, 0 deletions
diff --git a/info/mathtrip/src/hyper.tex b/info/mathtrip/src/hyper.tex new file mode 100644 index 0000000000..19a92f8293 --- /dev/null +++ b/info/mathtrip/src/hyper.tex @@ -0,0 +1,54 @@ +%This command provides the text for the hyperbolic function in +%the second part of the second column in page 4 +% +%This macro has one parameter +% 1) The width allowed to typeset the text +\newcommand\TFourHyperbolic[1]{% + \parbox[t]{#1}{% + \DisplaySpace{\TFourDisplaySpace}{\TFourDisplayShortSpace} + + \TFourTitle{Definitions:} + \begin{DisplayFormulae}{1}{0pt}{\TFourSkipFormulae}{\BigChar}{\StyleWithoutNumber} + \def\LineOfArray##1##2##3##4{\rule{0pt}{4ex plus .5ex minus 1ex}% + {##1}&=&{##2}&{##3}&=&{##4}\\} + \Fm{\begin{array}{l%Equal sign + @{\hspace{.1em}}c@{\hspace{.2em}}% + l% + l% + @{\hspace{.1em}}c@{\hspace{.2em}}% + l} + \LineOfArray{\sinh x}{\frac{e^x - e^{-x}}{2}}% + {\cosh x}{\frac{e^x + e^{-x}}{2}} + \LineOfArray{\tanh x}{\frac{e^x - e^{-x}}{e^x + e^{-x}}} + {\csch x}{\frac{1}{\sinh x}} + \LineOfArray{\sech x}{\frac{1}{\cosh x}} + {\coth x}{\frac{1}{\tanh x}} + \end{array}% + } + \end{DisplayFormulae} + + \TFourTitle{Identities:} + \AdjustSpace{1ex plus .5ex minus .5ex} + \begin{DisplayFormulae}{1}{0pt}{\TFourSkipFormulae}{\BigChar}{\StyleWithoutNumber} + \def\FmSep{\unskip\text{,}}%use a comma as separator for the formula + \Fm{\cosh^2 x - \sinh^2 x = 1} + \Fm{\tanh^2 x + \sech^2 x = 1} + \Fm{\coth^2 x - \csch^2 x = 1} + \Fm{\sinh (-x) = - \sinh x} + \Fm{\cosh (-x) = \cosh x} + \Fm{\tanh (-x) = - \tanh x} + \Fm{\sinh (x + y) = \sinh x \cosh y + \cosh x \sinh y} + \Fm{\cosh (x + y) = \cosh x \cosh y + \sinh x \sinh y} + \Fm{\sinh 2x = 2 \sinh x \cosh x} + \Fm{\cosh 2x = \cosh^2 x + \sinh^2 x} + \Fm{\cosh x + \sinh x = e^x} + \Fm{\cosh x - \sinh x = e^{-x}} + \def\FirstPart{(\cosh x + \sinh x)^n = \mbox{}} + \FmPartA{\FirstPart\cosh n x +} + \FmPartB{\FirstPart}{\sinh n x \MathRemark{n \in \Z}} + \Fm{2 \sinh^2 \tfrac{x}{2} = \cosh x - 1} + \def\FmSep{\unskip\text{.}} + \Fm{2 \cosh^2 \tfrac{x}{2} = \cosh x + 1} + \end{DisplayFormulae} + } +} |