x={ π+4nπ; (-1)ⁿ⁺¹·π/3+2nπ }, n∈Z
Объяснение:
x/2=t
cos2t+sint=0
1-2sin²t+sint=0
2sin²t-sint-1=0
2sin²t-sint-1=2sin²t-2sint+sint-1=2sint(sint-1)+(sint-1)=(sint-1)(2sint+1)
(sint-1)(2sint+1)=0
1) sint-1=0
sint=1
t=π/2+2nπ
x/2=π/2+2nπ
x=π+4nπ
2) 2sint+1=0
sint=-0,5
t=(-1)ⁿarcsin(-0,5)+nπ
t=(-1)ⁿ⁺¹·π/6+nπ
x/2=(-1)ⁿ⁺¹·π/6+nπ
x=(-1)ⁿ⁺¹·π/3+2nπ
x={ π+4nπ; (-1)ⁿ⁺¹·π/3+2nπ }, n∈Z
Объяснение:
x/2=t
cos2t+sint=0
1-2sin²t+sint=0
2sin²t-sint-1=0
2sin²t-sint-1=2sin²t-2sint+sint-1=2sint(sint-1)+(sint-1)=(sint-1)(2sint+1)
(sint-1)(2sint+1)=0
1) sint-1=0
sint=1
t=π/2+2nπ
x/2=π/2+2nπ
x=π+4nπ
2) 2sint+1=0
sint=-0,5
t=(-1)ⁿarcsin(-0,5)+nπ
t=(-1)ⁿ⁺¹·π/6+nπ
x/2=(-1)ⁿ⁺¹·π/6+nπ
x=(-1)ⁿ⁺¹·π/3+2nπ