Question

|sinx|=1 Чему равен икс? Решите, пожалуйста.

Answer 1

Раскрываем модуль:
1) sinx = - 1
x₁ = - π/2 + 2πk, k∈Z
2) sinx = 1
x₂ = π/2 + 2πn, n∈Z
Ответ: x₁ = - π/2 + 2πk, k∈Z ; x₂ = π/2 + 2πn, n∈Z

Answer 2

Solving the Equation |sin(x)| = 1

To solve the equation |sin(x)| = 1, we need to find the values of x that satisfy this equation. Let's break down the solution step by step.

1. We have the absolute value of sin(x) equal to 1. This means that sin(x) can be either 1 or -1, as the absolute value of both is 1.

2. We can write two separate equations based on the two possible values of sin(x): - sin(x) = 1 - sin(x) = -1

3. Let's solve the first equation, sin(x) = 1: - The solutions for sin(x) = 1 lie in the first and second quadrants of the unit circle, where sin(x) is positive. - The general solution for sin(x) = 1 is x = π/2 + 2πn, where n is an integer.

4. Now, let's solve the second equation, sin(x) = -1: - The solutions for sin(x) = -1 lie in the third and fourth quadrants of the unit circle, where sin(x) is negative. - The general solution for sin(x) = -1 is x = 3π/2 + 2πn, where n is an integer.

5. Combining the solutions from both equations, we have two general solutions: - x = π/2 + 2πn, where n is an integer - x = 3π/2 + 2πn, where n is an integer

These are the general solutions for the equation |sin(x)| = 1. They represent all the possible values of x that satisfy the equation.

Please note that the solutions are given in terms of radians. If you need the solutions in degrees, you can convert them using the formula: degrees = radians * (180/π).

I hope this helps! Let me know if you have any further questions.