Commit 845ed5f5 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 143775f5
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Stockage demo pour coordonnées non orthogonales.
figure à faire
$`u_1=u\cdot\cos(\alpha)`$
$`u^1=u\cdot\dfrac{\cos(a + \alpha)}{\cos(a)}`$
$`u_2=u\cdot\cos(\theta + \beta)=u\cdot\sin(a + \alpha)`$
$`u^2=u\cdot\dfrac{\sin(\alpha)}{\cos(a)}`$
$`v_1=v\cdot\cos(\theta + \alpha)`$
$`v^1=v\cdot\dfrac{\cos(a + \theta + \alpha)}{\cos(a)}`$
$`v_2=v\cdot\sin(a + \theta + \alpha)`$
$`v^2=v\cdot\dfrac{\sin(\theta + \alpha)}{\cos(a)}`$
$`u_1\,v^1\,+\, u_2\,v^2\,=u\cdot\cos(\alpha)\cdot v\cdot\dfrac{\cos(a + \theta + \alpha)}
{\cos(a)} + u\cdot\sin(a + \alpha) \cdot v\cdot\dfrac{\sin(\theta + \alpha)}{\cos(a)}`$
$`\quad= u\,v\,\dfrac{1}{\cos(a)} \,[cos(\alpha)\,\cos(a + \theta + \alpha)\,+\,\sin(a + \alpha)\,\sin(\theta + \alpha)]`$
$`\cos(a + \theta + \alpha)=\cos[a + (\theta + \alpha)]=\cos(a)\,\cos(\theta + \alpha)-\sin(a)\,\sin(\theta + \alpha)`$
$`\sin(a + \alpha)=\sin(a)\cos(\alpha)+\sin(\alpha)\cos(a)`$
$`\sin(\theta + \alpha)=\sin(\theta)\cos(\alpha)+\sin(\alpha)\cos(\theta)`$
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