Question

!!!Помогите найти область определения y=ctg(x+pi/6) С решением, пожалуйста

Answer 1

$sin(x+ \frac{ \pi }{6} ) \neq 0$
$(x+ \frac{ \pi }{6} ) \neq = \pi n,$ n∈Z
$x \neq - \frac{ \pi }{6} + \pi n,$ n∈Z

Answer 2

Finding the Domain of y = ctg(x + π/6)

To find the domain of the function y = ctg(x + π/6), we need to consider the values of x for which the function is defined.

The cotangent function, ctg(x), is defined for all real numbers except the values where the cosine function is equal to zero. The general formula for the cotangent function is ctg(x) = cos(x) / sin(x).

The cosine function, cos(x), is equal to zero at odd multiples of π/2. Therefore, the domain of the function y = ctg(x + π/6) will be all real numbers except the values of x for which sin(x + π/6) = 0.

Solution

To find the domain, we need to solve the equation sin(x + π/6) = 0.

sin(x + π/6) = 0 when x + π/6 = nπ, where n is an integer.

Solving for x, we get: x = nπ - π/6, where n is an integer.

This means that the domain of the function y = ctg(x + π/6) is all real numbers except x = nπ - π/6, where n is an integer.

Therefore, the domain of the function y = ctg(x + π/6) is all real numbers except x = nπ - π/6, where n is an integer.