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BlackSoul5
@BlackSoul5
July 2022
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Помогите решить задание!!!пожалуйста
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sedinalana
1-2sin²x-3sinx+1=0
sinx=a
2a²+3a-2=0
D=9+16=25
a1=(-3-5)/4=-2⇒sinx=-2<-1 нет решения
a2=(-3+5)/4=1/2⇒sinx=1/2
1)x=π/6+2πn,n∈z
-π≤π/6+2n≤π
-6≤1+12n≤6
-7≤12n≤5
-7/12≤n≤5/12
n=0⇒x=π/6
2)x=5π/6+2πk,k∈z
-π≤5π/6+2k≤π
-6≤5+12k≤6
-11≤12k≤1
-11/12≤k≤1/12
k=0⇒x=5π/6
2 votes
Thanks 1
BlackSoul5
спасибо большое!
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Answers & Comments
sinx=a
2a²+3a-2=0
D=9+16=25
a1=(-3-5)/4=-2⇒sinx=-2<-1 нет решения
a2=(-3+5)/4=1/2⇒sinx=1/2
1)x=π/6+2πn,n∈z
-π≤π/6+2n≤π
-6≤1+12n≤6
-7≤12n≤5
-7/12≤n≤5/12
n=0⇒x=π/6
2)x=5π/6+2πk,k∈z
-π≤5π/6+2k≤π
-6≤5+12k≤6
-11≤12k≤1
-11/12≤k≤1/12
k=0⇒x=5π/6