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author | Norbert Preining <norbert@preining.info> | 2022-10-02 03:04:14 +0000 |
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committer | Norbert Preining <norbert@preining.info> | 2022-10-02 03:04:14 +0000 |
commit | 097f244236b682cc77c6ecf25be4150091d8daf9 (patch) | |
tree | 26998e72d2b56a87033d9fb72923258fc93ebe53 /info/mathtrip/src/trig2.tex | |
parent | 4043e29dc8ac56047ac45f872a2ea1f3031b6b05 (diff) |
CTAN sync 202210020304
Diffstat (limited to 'info/mathtrip/src/trig2.tex')
-rw-r--r-- | info/mathtrip/src/trig2.tex | 65 |
1 files changed, 65 insertions, 0 deletions
diff --git a/info/mathtrip/src/trig2.tex b/info/mathtrip/src/trig2.tex new file mode 100644 index 0000000000..c8f69deb68 --- /dev/null +++ b/info/mathtrip/src/trig2.tex @@ -0,0 +1,65 @@ +%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} + }% +} |