Question

Помогите пожалуйста sin x=-корень из 2/2 ,x принадлежит [-pi;2pi] пожалуйстааа

Answer 1

Sinx=- $\frac{ \sqrt{2} }{2}$
x= - $\frac{ \pi }{4}$ +2$\pi$*n
x= - $\frac{ 3 \pi }{4}$ +2$\pi$*n, n - целое
на отрезке [-$\pi$; 2$\pi$] корни - x=  - $\frac{ \pi }{4}$ , x= - $\frac{ 3 \pi }{4}$ 
Ответ : x= - $\frac{ 3 \pi }{4}$ , - $\pi$ /4

Answer 2

Solving the Equation sin(x) = -√2/2

To solve the equation sin(x) = -√2/2, we can use the unit circle and the properties of the sine function.

The value -√2/2 corresponds to -45 degrees or -π/4 radians on the unit circle. This is one of the standard angles for which the sine function has a specific value.

So, we can express the solutions for sin(x) = -√2/2 as: x = -π/4 + 2kπ or x = π - π/4 + 2kπ, where k is an integer.

This means that the solutions for x within the interval [-π, 2π] are: x = -π/4, 7π/4

Let's verify this solution using the given equation and the specified interval.