Question

х принадлежит промежутку

Answer 1

sinx=-1

x=2pin-pi/2, n∈Z

[0; 4pi]

x1=(3/2)pi

x2=(7/2)pi

Answer 2

Finding the value of x within a given interval

To find the value of x within a given interval, we need to consider the information provided in the search results. Let's analyze the snippets to determine the value of x.

From Source we have the equation \(7\sin x\), where \(\cos x = \frac{2\sqrt6}{7}\) and \(x\) belongs to the interval \((\pi:\frac{3\pi}{2})\).

From Source we have the equation \(\sqrt{2x^2 - 4x - 6} = x\), and \(x\) belongs to the interval \([-2;4]\).

Unfortunately, the other search results do not provide relevant information for finding the value of x within a given interval.

Calculating the value of x

Let's solve the equations to find the value of x within the given intervals.

From Source we have \(7\sin x\) and \(\cos x = \frac{2\sqrt6}{7}\). We can use the identity \(\sin^2x + \cos^2x = 1\) to solve for \(\sin x\). Rearranging the equation, we have \(\sin^2x = 1 - \cos^2x\). Substituting the value of \(\cos x\), we get \(\sin^2x = 1 - \left(\frac{2\sqrt6}{7}\right)^2\). Simplifying further, we have \(\sin^2x = 1 - \frac{24}{49}\), which gives us \(\sin^2x = \frac{25}{49}\). Taking the square root of both sides, we find \(\sin x = \pm\frac{5}{7}\). Since \(x\) belongs to the interval \((\pi:\frac{3\pi}{2})\), we can conclude that \(x = -\frac{5}{7}\) [[1]](https://umschool.net/library/matematika/formuly-trigonometrii-i-prostejshie-uravneniya/).

From Source we have the equation \(\sqrt{2x^2 - 4x - 6} = x\), and \(x\) belongs to the interval \([-2;4]\). To solve this equation, we need to square both sides. Squaring the equation, we get \(2x^2 - 4x - 6 = x^2\). Rearranging the terms, we have \(x^2 - 4x - 6 = 0\). We can solve this quadratic equation using factoring, completing the square, or the quadratic formula. However, since the search results do not provide enough information to determine the exact value of x, we cannot find the solution within the given interval.

In conclusion, from the available information, we can determine that \(x = -\frac{5}{7}\) within the interval \((\pi:\frac{3\pi}{2})\). However, we cannot determine the value of x within the interval \([-2;4]\) based on the provided search results.