contents/trigonometry.tex : added hyperbolic formulas

contents/computer_science.tex

@@ -12,7 +12,6 @@
 \SetAlgoLined
 \SetNoFillComment
 \tcc{This is a comment}
-\vspace{3mm}
 some code here\;
 $x \leftarrow 0$\;
 $y \leftarrow 0$\;
@@ -35,16 +34,28 @@ $y \leftarrow 0$\;
 \caption{what}
 \end{algorithm}
 
+\langsection{Exemple en Haskell}{Haskell example}
+\begin{lstlisting}[language=Haskell]
+fibonacci :: Int -> Int
+fibonacci 0 = 0
+fibonacci 1 = 1
+fibonacci n = fibonacci (n - 1) + fibonacci (n - 2)
+\end{lstlisting}
+
 \langsection{Exemple en Python}{Python example}
 \begin{lstlisting}[language=Python]
-def fnc(a, b):
+def fibonacci(n: int) -> int:
-	return a + b
+	if n == 0 or n == 1:
+		return n
+	return fibonacci(n - 1) + fibonacci(n - 2)
 \end{lstlisting}
 
 \langsection{Exemple en C}{C example}
 \begin{lstlisting}[language=C]
-int fnc(int a, int b){
+int fibonacci(const int n){
-	return a + b;
+	if (n == 0 || n == 1)
+		return n;
+	return fibonacci(n - 1) + fibonacci(n - 2);
 }
 \end{lstlisting}
 

contents/trigonometry.tex

@@ -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}
+
+$tanh\ x = \frac{sinh\ x}{cosh\ x} = \frac{e^x - e^{-x}}{e^x + e^{-x}} = \frac{e^{2x} - 1}{e^{2x} + 1}$