Решите неравенства: 1) 2sin²x-3√2sinx+2>0; 2) 4sin²x+5sinx+2cos²x>0. Created by alexclark169. algebra-ru

Решите неравенства: 1) 2sin²x-3√2sinx+2>0; 2) 4sin²x+5sinx+2cos²x>0...

July 2022 1 13 Report

Решите неравенства: 1) 2sin²x-3√2sinx+2>0;
2) 4sin²x+5sinx+2cos²x>0

Answers & Comments

sedinalana 1) 2sin²x-3√2sinx+2>0
sinx=t
2t²-3√2t+2>0
D=18-16=2
t1=(3√2-√2)/4=√2/2
t2=(3√2+√2)/4=√2
t<√2/2⇒sinx<√2/2⇒x∈(3π/4+2πk;9π/4+2πk.k∈z)
t>√2⇒sinx>√2 нет решения

2) 4sin²x+5sinx+2cos²x>0
4sin²x+5sinx+2-2sin²x>0
2sin²x+5sinx+2>0
sinx=t
2t²+5t+2>0
D=25-16=9
t1=(-5-3)/4=-2
t2=(-5+3)/4=-1/2
t<-2⇒sinx<-2 нет решения
t>-1/2⇒sinx>-1/2⇒x∈(-π/6+2πk;7π/6+2πk,k∈z)

0 votes Thanks 1

alexclark169 А почему в 1) "t<√2/2⇒sinx<√2/2⇒x∈(3π/4+2πk;9π/4+2πk.k∈z)", там разве не t>√2/2, sinx>√2/2?

Answers & Comments

pomogite pozhalujsta napisat pravilno pismo otvet vot zadanie i pismo na ko

napryazhennost elektricheskogo polya sozdavaemogo tochechnym zaryadom v srede vychisl

reshit sin42x cos42x esli tgx05

reshit sin190 cos40 cos130 cos10 ne po tablice

2 najti ab522d3fb929215f6e1c6d42b593d865e9 77549

dx delta ef ot iks nulevogo delit delta iks

srochno opredelite slova v kotoryh pered e proiznositsya tverdyj soglasnyj zvuk

1 dajte nazvanie veshestvu po sistematicheskoj nomenklature ch3 hco 2 isklyuchi

dokazhite chto zadannaya funkciya vozrastaet na vsej chislovoj pryamoj yx7 7x

complete the sentences with the correct question tags. 1) you haven't been to Br...

рекомендуемые вопросы

Helpful Links

Helpful Social