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July 2022 1 16 Report

упростите выражение:
sin(п/2-t);
cos(90°-a)
sin(360°-a)
sin(270°-a)
cos(180°-a)
вычислите с помощью формул приведения:
cos 330°;ctg 315°
sin(-7п)+2cos31п/3-tg7п/4
tg1800°-sin495°+cos945°
cos(-9п)+2sin(-49п/6)-ctg(-21п/4)

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Anastsiia

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$sin( \pi /2-t) = cost \\ cos(90^o-\alpha) = sin\alpha \\ sin(360^0-\alpha) = -sin\alpha \\ 
sin(270^o-\alpha) = -cos\alpha \\ cos(180^o-\alpha) =-cos\alpha \\ 
sin(-7 \pi )+2cos31 \pi /3-tg7 \pi /4 = \\ =-sin \pi +2cos(10\pi+\pi /3)-tg( \pi +3 \pi /4)=0+2cos \pi /3-tg3 \pi /4= \\ =2* \frac{1}{2}-(-1)=1+1=2 \\ tg1800^o-sin495^o+cos945^o = tg10 \pi -sin(360^o+135^o)+ \\ +cos(5 \pi + \pi /4)=0- \sqrt{2} /2-\sqrt{2} /2= \sqrt{2}$
$cos(-9 \pi )+2sin(-49 \pi /6)-ctg(-21 \pi /4)= \\ =cos(8 \pi + \pi )-2sin(8 \pi+ \pi /6)+ctg(5 \pi + \pi /4)= \\ =-1-2* \frac{1}{2}+1=-1$

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