№1 а) Sinx = √3/2х = (-1)^n arcSin √3/2 + nπ, n ∈Zx = (-1)^n·π/3 + πn , n ∈Zб) Cos x = 1x = 2πn , n∈Zв) tgx = 0x = πk , k ∈Zг) 3Sin x -1 = 13Sin x = 2Sin x = 2/3x = (-1)^n arcSin(2/3) + nπ , n ∈Zд) arcCos(9x -11) = π/69x -11 = √3/2x = √3/18 + 11/9е)Сtg x -10 = 1Ctgx = 11x = arcCtg11 + πk , k ∈Zж) Sin(x + π/4) = 1/2x + π/4 = (-1)^n π/6 + nπ, n ∈Zx = (-1)^n π/6 + πn - π/4 , n ∈Zз) Cos x = 5нет решенийи)Sin²x - Sin x -2 = 0решаем как квадратное:а) Sin x = 2 или б) Sin x = -1нет решений x = -π/2 + 2πk , k ∈Z№2 а) Cos x > 1/2-π/3 + 2πk < x < π/3 + 2πk , k ∈Zб) Sin x ≤ √3/2π/3 + 2πk ≤ x ≤ 2π/3 + 2πk , k ∈Zв) Cos x > 2нет решений№3 а) 2Sinx +1 = 0 [ 0, 3π]Sin x = -1/2x = (-1)^(n+1) π/6 + nπ, n ∈Z1) n = 0x = -π/6 2) n=1x = π/6 + π = 7π/63) n = 2x = -π/6 +2π = 11π/64) n = 3x = π/6 + 3πб) 4tgx = 4 [ -π, 2π]tgx = 1x = π/4 + πk , k∈Z1) k = -1x = π/4 - π =
-3π/42) k = 0x =
π/43) k = 1x = π/4 + π =
5π/44) k = 2x = π/4 + 2π = 9π/4