Question

Ctgx если sin x= -1/√3 ,Х =( П;3П/2)

Answer 1

sin x = 1/3  

x = arcsin 1/3 = 19 градусов 28 минут 16 секунд с хвостиком +2 Пи * n, где n принадлежит Z

Answer 2

To find the value of cotangent (ctgx) when sin(x) = -1/√3 and x lies in the interval (π, 3π/2), we first need to find the cosine (cos(x)) value using the given sine value. Then we can calculate the cotangent.

1. Given sin(x) = -1/√3, we can find cos(x) using the Pythagorean trigonometric identity: sin^2(x) + cos^2(x) = 1.

sin^2(x) + cos^2(x) = (-1/√3)^2 + cos^2(x) = 1.

cos^2(x) = 1 - (-1/√3)^2 = 1 - 1/3 = 2/3.

cos(x) = ±√(2/3). Since x is in the interval (π, 3π/2), cos(x) is negative in this interval. Therefore, cos(x) = -√(2/3).

2. Now that we have cos(x), we can calculate cot(x) using the reciprocal relationship between cotangent and tangent: cot(x) = 1/tan(x).

cot(x) = 1/tan(x) = 1/(sin(x)/cos(x)) = cos(x)/sin(x).

cot(x) = (-√(2/3))/(-1/√3) = √(2/3).

So, cot(x) = √(2/3) when sin(x) = -1/√3 and x lies in the interval (π, 3π/2).