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contents/trigonometry.tex : added hyperbolic formulas

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saundersp 2024-07-11 22:50:20 +02:00
parent b9ca4eaa67
commit c1a6223f54
1 changed files with 15 additions and 3 deletions
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contents/trigonometry.tex
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@ -23,7 +23,7 @@ $\cos\frac{\pi}{6} = \frac{\sqrt{3}}{2}$
$\cos\frac{\pi}{3} = \frac{1}{2}$
$\forall (a,b) \in \R^2$
$\forall (a,b) \in \R$
$\cos(a + b) = \cos a \cos b + \sin a \sin b$
@ -46,7 +46,7 @@ $\sin \frac{\pi}{2} = 1$
%$\sin(\frac{\pi}{2} + t) = -\cos(t)$
$\forall (a,b) \in \R^2$
$\forall (a,b) \in \R$
$\sin(a + b) = \sin a \cos b + \sin b \cos a$
@ -76,8 +76,20 @@ $\tan(a - b) = \frac{\tan(a) - \tan(b)}{1 + \tan(a)\tan(b)}$
\subsection{Combinaisons}
%TODO Complete subsection
$\forall (a,b) \in \R^2$
$\forall (a,b) \in \R$
$\sin a \cos b = \frac{\sin(a + b) + \sin(a - b)}{2}$
\langsection{Fonctions hyperboliques}{Hyperbolic functions}
\subsection{cosh}
$cosh\ x = \frac{e^x + e^{-x}}{2} = \frac{e^{2x} + 1}{2e^x} = \frac{1 + e^{-2x}}{2e^{-x}}$
\subsection{sinh}
$sinh\ x = \frac{e^x - e^{-x}}{2} = \frac{e^{2x} - 1}{2e^x} = \frac{1 - e^{-2x}}{2e^{-x}}$
\subsection{tanh}
$tanh\ x = \frac{sinh\ x}{cosh\ x} = \frac{e^x - e^{-x}}{e^x + e^{-x}} = \frac{e^{2x} - 1}{e^{2x} + 1}$