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radmir142314233
@radmir142314233
July 2022
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Решить уравнение:
6sin^2x - 11cosx - 10 = 0
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MizoriesKun
Verified answer
6sin^2x - 11cosx - 10 = 0 sin^2x=(1-cosx^2x) ,
6*(1-cosx^2x) - 11cosx - 10 = 0
6- 6cosx^2x - 11cosx - 10 = 0
6cosx^2x + 11cosx +4= 0 замена cosx=а
6а²+11а+4=0
D=121- 96=25 √D=5
a₁=(-11+5)/12=-1/2
a₂=(-11-5)/12=-16/12= - 4/3
cos(x)=-1/2 cos(x)=-4/3
х= 2π/3+2πn₁ n₁∈Z x= cos⁻¹(-4/3)+2πn n∈Z
x=4π/3+2πn₂ n₂∈Z x= 2πn - cos⁻¹(-4/3) n∈Z
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radmir142314233
Спасибо огромное!:)
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Answers & Comments
Verified answer
6sin^2x - 11cosx - 10 = 0 sin^2x=(1-cosx^2x) ,6*(1-cosx^2x) - 11cosx - 10 = 0
6- 6cosx^2x - 11cosx - 10 = 0
6cosx^2x + 11cosx +4= 0 замена cosx=а
6а²+11а+4=0
D=121- 96=25 √D=5
a₁=(-11+5)/12=-1/2
a₂=(-11-5)/12=-16/12= - 4/3
cos(x)=-1/2 cos(x)=-4/3
х= 2π/3+2πn₁ n₁∈Z x= cos⁻¹(-4/3)+2πn n∈Z
x=4π/3+2πn₂ n₂∈Z x= 2πn - cos⁻¹(-4/3) n∈Z