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zena1102
@zena1102
July 2022
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rskopov
Решение:
1) sin(п+п/4)=-sqrt(2)/2
tg(п+п/6)=tg(п/6)=1/sqrt(3)
sqrt(3)/2-1
-1*(-sqrt(2)/2)-1/2*sqrt(3)=(sqrt(2)-sqrt(3))/2
sin(180-30)-(-1)*0=sin30=1/2
2.cos^2t-sin^2t/(-1)=1
3. a) t=(-1)^kП/6+Пk
б) sin(П/2+t)=cost=-sqrt(3)/2
t=П+-П/6+2Пk
4. a) cos(270-t)=-sint=-3/5
ctgt=-3/4
(1-sin^2t)/sin^2t=9/16
sin^2t=9/25
sint=3/5
cost=-4/5
cos(П+t)=-cost=4/5
5. sin6<0 sin4<0 cos6-cos7=2sin1/2sin13/2>0
cos6>cos7>sin6 sin6-sin4=2sin1cos5>0
sin6>sin4 sin4<sin6<cos7<cos6.
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Answers & Comments
1) sin(п+п/4)=-sqrt(2)/2
tg(п+п/6)=tg(п/6)=1/sqrt(3)
sqrt(3)/2-1
-1*(-sqrt(2)/2)-1/2*sqrt(3)=(sqrt(2)-sqrt(3))/2
sin(180-30)-(-1)*0=sin30=1/2
2.cos^2t-sin^2t/(-1)=1
3. a) t=(-1)^kП/6+Пk
б) sin(П/2+t)=cost=-sqrt(3)/2
t=П+-П/6+2Пk
4. a) cos(270-t)=-sint=-3/5
ctgt=-3/4
(1-sin^2t)/sin^2t=9/16
sin^2t=9/25
sint=3/5
cost=-4/5
cos(П+t)=-cost=4/5
5. sin6<0 sin4<0 cos6-cos7=2sin1/2sin13/2>0
cos6>cos7>sin6 sin6-sin4=2sin1cos5>0
sin6>sin4 sin4<sin6<cos7<cos6.