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Diffstat (limited to 'info/mathtrip/src/trig1.tex')
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diff --git a/info/mathtrip/src/trig1.tex b/info/mathtrip/src/trig1.tex new file mode 100644 index 0000000000..ec8f09a657 --- /dev/null +++ b/info/mathtrip/src/trig1.tex @@ -0,0 +1,84 @@ +%This command provides the text to be typeset on the +%first column of page 4. The first trigonometric +%formulae +% +%The macro has one parameter: +% 1) The width of math text +\newcommand\TFourTrigOne[1]{% + \parbox[t]{#1}{% + \DisplaySpace{\TFourDisplaySpace}{\TFourDisplayShortSpace} + %The column is narrow, ragged right looks nicer + \raggedright + + \input{unit.tex} + \hspace{-.85em plus .1em minus .1em}\usebox\UnitBox + + \TFourTitle{Pythagorean theorem:} + \begin{DisplayFormulae}{1}{0pt}{3ex plus 1ex minus .5ex}{\SmallChar}{\StyleWithoutNumber} + \Fm{C^2 = A^2 + B^2}. + \end{DisplayFormulae} + + \TFourTitle{Definitions:} + \begin{DisplayFormulae}{1}{0pt}{3ex plus 1ex minus .5ex}{\BigChar}{\StyleWithoutNumber} + \def\LineOfArray##1##2##3##4{% + \rule{0pt}{4ex plus 1ex minus .5ex}% + {##1}&=&{##2}&{##3}&=&{##4}\\} + \Fm{\begin{array}{l%Equal sign + @{\hspace{.1em}}c@{\hspace{.2em}}% + l% + l%Equal sign + @{\hspace{.1em}}c@{\hspace{.2em}}% + l} + \LineOfArray{\sin a}{\frac{A}{C}}{\cos a}{\frac{B}{C}} + \LineOfArray{\csc a}{\frac{C}{A}}{\sec a}{\frac{C}{B}} + \LineOfArray{\tan a}{\frac{\sin a}{\cos a} = \frac{A}{B}} + {\cot a}{\frac{\cos a}{\sin a}=\frac{B}{A}} + \end{array}% + } + \end{DisplayFormulae} + + \TFourTitle{Area, radius of inscribed circle:} + \begin{DisplayFormulae}{1}{0pt}{3ex plus 1ex minus .5ex}{\SmallChar}{\StyleWithoutNumber} + \Fm{\tfrac{1}{2} A B} + \Fm{\frac{A B}{A + B + C}} + \end{DisplayFormulae} + + \TFourTitle{Identities:} + \begin{DisplayFormulae}{1}{0pt}{\TFourSkipFormulae}{\BigChar}{\StyleWithoutNumber} + \def\FmSep{\text{,}} + \Fm{\sin x = \frac{1}{\csc x}} + \Fm{\cos x = \frac{1}{\sec x}} + \Fm{\tan x = \frac{1}{\cot x}} + \Fm{\sin^2 x + \cos^2 x = 1} + \Fm{1 + \tan^2 x = \sec^2 x} + \Fm{1 + \cot^2 x = \csc^2 x} + \Fm{\sin x = \cos \left(\tfrac{\pi}{2} - x\right)} + \Fm{\sin x = \sin (\pi - x)} + \Fm{\cos x = - \cos (\pi - x)} + \Fm{\tan x = \cot \left(\tfrac{\pi}{2} - x\right)} + \Fm{\cot x = - \cot (\pi - x)} + \Fm{\csc x = \cot \tfrac{x}{2} - \cot x} + \Fm{\sin (x \pm y) = \sin x \cos y \pm \cos x \sin y} + \Fm{\cos (x \pm y) = \cos x \cos y \mp \sin x \sin y} + \Fm{\tan (x \pm y) = \frac{\tan x \pm \tan y}{1 \mp \tan x \tan y}} + \Fm{\sin 2 x = 2 \sin x \cos x} + \Fm{\sin 2 x = \frac{2 \tan x}{1 + \tan^2 x}} + \Fm{\cot (x \pm y) = \frac{\cot x \cot y \mp 1}{\cot x \pm \cot y }} + \Fm{\cos 2 x = \cos^2 x - \sin^2 x} + \Fm{\cos 2 x = 2 \cos^2 x - 1} + \Fm{\cos 2 x = 1 - 2 \sin^2 x} + \Fm{\cos 2 x = \frac{1 - \tan^2 x}{1 + \tan^2 x}} + \Fm{\tan 2 x = \frac{2 \tan x}{1 - \tan^2 x}} + \Fm{\cot 2 x = \frac{\cot^2 x - 1}{2 \cot x}} + \Fm{\sin (x + y) \sin (x - y) = \sin^2 x - \sin^2 y} + \def\FmSep{\text{.}} + \Fm{\cos (x + y) \cos (x - y) = \cos^2 x - \sin^2 y} + \end{DisplayFormulae} + + \TFourTitle{Euler's equation:} + \begin{DisplayFormulae}{1}{0pt}{3ex plus 1ex minus .5ex}{\SmallChar}{\StyleWithoutNumber} + \Fm{e^{i x} = \cos x + i \sin x}, + \Fm{e^{i \pi} + 1= 0}. + \end{DisplayFormulae} + } +} |