Question

Tgx=корень из 3 нужно подробное решение) всем спасибо)

Answer 1

Tgx=√3
   x=П/3 + Пn

По таблице tg √3 = 60° и равен П/3 

Ответ: П/3 + Пn

Answer 2

Solution for tgx = √3

To solve the equation \(tgx = \sqrt{3}\), we can use the properties of the tangent function to find the values of x.

1. Finding the Values of x for tgx = -1: - When \(tgx = -1\), we have the solution: \[x = -\frac{\pi}{4} + \pi n\] where \(n\) is an integer.

2. Finding the Values of x for tgx = 1/2: - When \(tgx = \frac{1}{2}\), the solution is: \[x = \arctan\left(\frac{1}{2}\right) + \pi n\] where \(n\) is an integer and the principal value of \(\arctan\left(\frac{1}{2}\right)\) lies in the interval \(\left[\frac{3\pi}{2}, \frac{5\pi}{2}\right]\) [[1]](https://youclever.org/book/trigonometricheskie-uravneniya-1/).

3. Using the Solution for tgx in Another Equation: - If we substitute the value of \(tgx\) into the equation \(\frac{1}{{tg^2x}} + \frac{3}{\sin x} + 3 = 0\), we can solve for the values of \(x\) within the interval \(\left[2\pi, \frac{7\pi}{2}\right]\).

These steps provide the solutions for the equation \(tgx = \sqrt{3}\) and demonstrate how to find the values of \(x\) based on the given trigonometric equation.