summaryrefslogtreecommitdiff
path: root/info/mathtrip/src/trig2.tex
diff options
context:
space:
mode:
Diffstat (limited to 'info/mathtrip/src/trig2.tex')
-rw-r--r--info/mathtrip/src/trig2.tex65
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}
+ }%
+}