2sin^3x+3 sin^2x+sinx=0 -2п -п

Question

2sin^3x+3 sin^2x+sinx=0 -2п -п

Answer 1

Sinx(2sin^2x + 3sinx + 1) = 0
sinx = 0
x1 = πn, n∈Z
2sin^2x + 3sinx + 1 = 0
D= 9 -4*2*1 = 1
sinx = (-3-1)/2= -2  не удовлетворяет условию;  I sinx I ≤1
sinx = (-3+1)/2 = -1
x2 = -π/2 + 2πk,k∈Z