Question

Simplifique A = sen (11 − x ) + cos (7 − x ), para x =  / 3 .

por favor o quanto antes

Answer 1

$sen(11\pi +x) +cos(7\pi -x)\\x=\pi /3\\\\\\=sen(11\pi +\pi /3)+cos(7\pi -\pi /3)\\\\=sen11\pi .cos \pi /3 + sen\pi /3.cos11\pi + cos7\pi .cos\pi /3+sen7\pi .sen\pi /3$

Temos que:

sen 11π= 0

cos 11π=-1

sen π/3=$\sqrt{3} /2$

cos π/3=$1/2$

sen 7π = 0

cos 7π=-1

Assim:

$sen11\pi .cos \pi /3 + sen\pi /3.cos11\pi + cos7\pi .cos\pi /3+sen7\pi .sen\pi /3\\\\=0+(\sqrt{3}/2).(-1)+(-1).(1/2)+0$

$-\sqrt{3}/2-1/2= \frac{-\sqrt{3}-1 }{2}$

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