По теореме синусов (расширенной):
a/sin(A)=2R⇒R=a/(2sin(A))=90/sin(20°)≈<span>263.14</span>
cos x/3<√2/2 π/4+2πn<x/3<7π/4+2πn n∈z
3π/4+6πn<x<21π/4+6πn. n∈z
ответ x∈(3π/4+6πn. 21π/4+6πn) n∈z
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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
A1=-6 a2=-2
d=a2-a1=-2+6=4
a16=a1+15d=-6+60=54