Question

Sin x= - корень из 3/2 напишите серию корней

Answer 1

$x= (-1)^{n} * arcsin a + \pi n; x= (-1)^{n}*(- \pi /3)+ \pi n$

Answer 2

Solving the Equation sin(x) = √3/2

To solve the equation sin(x) = √3/2, we need to find the values of x that satisfy this equation. Let's break down the solution step by step:

1. Start with the equation sin(x) = √3/2. 2. We can rewrite √3/2 as sin(π/3) because sin(π/3) = √3/2. 3. So, the equation becomes sin(x) = sin(π/3). 4. Using the identity sin(a) = sin(b), we can write x = π/3 + 2πn, where n is an integer. 5. Simplifying further, we have x = π/3 + 2πn, where n ∈ Z.

Series of Roots

The series of roots for the equation sin(x) = √3/2 can be expressed as:

1. x = π/3 + 2πn, where n ∈ Z. 2. x = π/3 + 2πn, where n ∈ Z.

In summary, the series of roots for the equation sin(x) = √3/2 is x = π/3 + 2πn, where n is an integer.

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