Bonsoir ;
Commençons par l'exercice n° 3 .
1)
[tex]E(0) = cos(0+\pi) - sin(0+\dfrac{\pi}{2})+2cos(0) \\\\ = cos(\pi) - sin(\dfrac{\pi}{2})+2 = -1-1+2= 0 .[/tex]
[tex]E(\dfrac{\pi}{2}) = cos(\dfrac{\pi}{2}+\pi) - sin(\dfrac{\pi}{2}+\dfrac{\pi}{2})+2cos(\dfrac{\pi}{2}) \\\\ = cos(\dfrac{3\pi}{2}) - sin(\pi)+0 = 0-0+0 = 0 .[/tex]
[tex]E(\pi) = cos(\pi+\pi) - sin(\pi+\dfrac{\pi}{2})+2cos(\pi) \\\\ = cos(2\pi) + 1-2 = 1+1-2= 0 .[/tex]
2)
[tex]\textit{On a : } sin(t+\dfrac{\pi}{2}) = cos(t) \textit{ et } cos(t+\pi) = -cos(t) ,\\\\ \textit{donc : } E(t) = cos(t+\pi)-sin(t+\dfrac{\pi}{2})+2cos(t) \\\\ = -cos(t) -cos(t) + 2cos(t) = 0 .[/tex]
