1) Sin7π/6 = Sin(π + π/6) = - Sinπ/6 = -1/2
2) Sinx +Sin3x = Sin2x +Sin4x
2Sin2xCosx = 2Sin3xCosx
Sin2xCosx - Sin3xCosx = 0
Cosx(Sin2x - Sin3x) = 0
Cosx = 0 Sin2x - Sin3x = 0
x = π/2 + πk , k ∈Z -2Sin(0,5x)Cos2,5x = 0
Sin 0,5x = 0 или Cos2,5x = 0
0,5x = πn , n∈Z 2,5x = π/2 + πm, m ∈Z
x = 2πn, n ∈Z x = π/5 + 2πm/5, m ∈Z
3) 8Sin²x + 6Cosx -9 = 0
8(1 - Cos²x) +6Cosx -9 = 0
8 - 8Cos²x +6Cosx -9 = 0
8Cos²x -6Cosx +1 = 0
a) Cosx = 1/2 б) Cosx = 1/4
x = +-π/3 + 2πk , k ∈Z x = +-arcCos1/4 + 2πn , n∈Z
4)Sinα = 0,6
Cos²α = 1 - Sin²α = 1 - 0,36 = 0,64
Cosα = 0,8
5) 2Sin²x -2Cos²x -√2 = 0
Sin²x - Cos²x = √2/2
-Cos2x = √2/2
Cos2x = -√2/2
2x = +-arcCos(-√2/2) + 2πk , k ∈Z
2x = +-3π/4 + 2πk , k ∈Z
x = +-3π/8 + πk , k ∈Z