Question

Sinx *sin3x =0 решение

Answer 1

sinx *sin3x =0
1) sin x = 0
    x₁ = πn
2) sin 3x = 0
    3x = πk
    x₂ = πk/3

Ответ: x₁ = πn; x₂ = πk/3;  n,k ∈ Z

Answer 2

To find the solutions to the equation sin(x) * sin(3x) = 0, we need to determine the values of x that make the left-hand side of the equation equal to zero.

The equation will be true if either sin(x) = 0 or sin(3x) = 0 or both are equal to zero.

1. sin(x) = 0: When sin(x) = 0, x can take the values of integer multiples of π (pi), since the sine function is zero at these points: x = 0, π, 2π, 3π, ...

2. sin(3x) = 0: When sin(3x) = 0, 3x can take the values of odd multiples of π/2, since sin(π/2) = 1, and sin(-π/2) = -1: 3x = π/2, 3π/2, 5π/2, ...

Now, to find the values of x, we divide each value of 3x by 3: x = π/6, π/2, 5π/6, ...

So the solutions to the equation sin(x) * sin(3x) = 0 are: x = 0, π, 2π, 3π, π/6, π/2, 5π/6, ...