Question

5 sin 11п/12 cos 11п/12

Answer 1

$5cdot sindfrac{11pi}{12} cdot cosdfrac{11pi}{12} =2,5cdot Big(2cdot sindfrac{11pi}{12} cdot cosdfrac{11pi}{12}Big) =\\=2,5cdot sinBig(2cdot dfrac{11pi}{12}Big)=2,5cdot sindfrac{11pi}{6}=\\=2,5cdot sinBig(dfrac{12pi-pi}{6}Big)=2,5cdot sinBig(2pi-dfrac{pi}{6}Big)=\\=2,5cdot sin Big(-dfrac{pi}{6}Big)=-2,5cdot sindfrac{pi}{6}=-2,5cdot dfrac{1}{2}=boxed{boldsymbol{-1,25}}$

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Использованы формулы

$2cdot sin~alpha cdot cos~alpha = sin (2alpha)\\sin(2pi-alpha)=sin(-alpha)=-sin~alpha$