Commit 43255427 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent e13e3076
Pipeline #15579 canceled with stage
...@@ -76,6 +76,10 @@ $`\begin{align} U(&x,t) = U_1(x,t) + U_2(x,t) \\ ...@@ -76,6 +76,10 @@ $`\begin{align} U(&x,t) = U_1(x,t) + U_2(x,t) \\
&=A\;\big[\,\underbrace{cos(\alpha ')\,cos\Big(\dfrac{\varphi_1-\varphi_2}{2}\Big)\,-\,sin(\alpha ')\,sin\Big(\dfrac{\varphi_1-\varphi_2}{2}}_{\text{car }cos(a+b)\;=\;cos\,a\,cos\,b\;-\;sin\,a\,sin\,b}\big)\\ &=A\;\big[\,\underbrace{cos(\alpha ')\,cos\Big(\dfrac{\varphi_1-\varphi_2}{2}\Big)\,-\,sin(\alpha ')\,sin\Big(\dfrac{\varphi_1-\varphi_2}{2}}_{\text{car }cos(a+b)\;=\;cos\,a\,cos\,b\;-\;sin\,a\,sin\,b}\big)\\
&\quad + \underbrace{cos(\alpha ')\,cos\Big(\dfrac{\varphi_1-\varphi_2}{2}\Big)\,+\,sin(\alpha ')\,sin\Big(\dfrac{\varphi_1-\varphi_2}{2}}_{\text{car }cos(a-b)\;=\;cos\,a\,cos\,b\;+\;sin\,a\,sin\,b}\big)\,\Big]\\ &\quad + \underbrace{cos(\alpha ')\,cos\Big(\dfrac{\varphi_1-\varphi_2}{2}\Big)\,+\,sin(\alpha ')\,sin\Big(\dfrac{\varphi_1-\varphi_2}{2}}_{\text{car }cos(a-b)\;=\;cos\,a\,cos\,b\;+\;sin\,a\,sin\,b}\big)\,\Big]\\
&\\ &\\
&=2\,A\cdot cos(\alpha ')\,cos\Big(\dfrac{\varphi_1-\varphi_2}{2}\Big)\\
&\\
&=\underbrace{2\,A\cdot cos\Big(\dfrac{\varphi_1-\varphi_2}{2}\Big)}_{\text{amplitude de l'onde résultante} \cdot \underbrace{cos\Big(\alpha + \dfrac{\varphi_1+\varphi_1}{2}\Big)}_{\text{pulsation }\omega\text{ inchangée}\\
&\\
\end{align}`$ \end{align}`$
......
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