Question

Sin 3x= -√3/2 Hhhhhhbbbb

Answer 1

Ответ:

sin (П-3x=-√3/2

3x=arcsin -√3/2

П-3x=arcsin -√3/2

3x=-П/3

П-3x = -П/3

3x= -П/3 + 2ПK, k€z

П-3х = -П/3 +2Пк, к€z

ответ: x= -П/9 + 2ПК/3, к€z

x=4П/9 - 2Пк/3, к€z

Answer 2

It seems like you've written an equation: sin(3x) = -√3/2. To solve this equation for x, we'll find the values of x that satisfy it. Here's the step-by-step solution:

1. First, let's find the reference angle for which sin is equal to -√3/2. The reference angle for sin is 60 degrees or π/3 radians.

2. Now, we know that the general form of sin(θ) is sin(θ) = sin(360°n + θ), where n is an integer. We can use this to find the solutions for sin(3x) = -√3/2.

3. Setting 3x equal to the reference angle π/3 and solving for x: 3x = π/3 x = π/9

4. However, sin has a periodicity of 360 degrees or 2π radians, so there will be multiple solutions. We can find other solutions by adding multiples of the period to our initial solution:

x = π/9 + 2π/3 = π/9 + 2π/3 = 5π/9 x = π/9 + 4π/3 = π/9 + 4π/3 = 7π/9

And so on...

So, the general solution for sin(3x) = -√3/2 is: x = π/9 + 2πn/3, where n is an integer.

Please note that this is a general solution, and there are infinitely many values of x that satisfy the equation.