Question

Сtg α = ? sin α =1/2, π/2<α<π

Answer 1

$sina=\frac{1}{2}\\\\\frac{\pi}{2}$

Answer 2

Ответ: во вложении Пошаговое объяснение:

Answer 3

To find the value of the cotangent (ctg) of α, we can use the relationship between trigonometric functions:

ctg(α) = 1 / tan(α)

Since we are given that sin(α) = 1/2, we can use the Pythagorean identity to find cos(α):

sin²(α) + cos²(α) = 1 (1/2)² + cos²(α) = 1 1/4 + cos²(α) = 1 cos²(α) = 1 - 1/4 cos²(α) = 3/4

cos(α) = ±√(3/4) = ±√3/2

Since α is in the second quadrant (π/2 < α < π), the cosine value is negative. Thus, cos(α) = -√3/2.

Now, we can find the tangent:

tan(α) = sin(α) / cos(α) tan(α) = (1/2) / (-√3/2) tan(α) = -(1/2) * (2/√3) tan(α) = -√3/3

Finally, we can find the cotangent:

ctg(α) = 1 / tan(α) ctg(α) = 1 / (-√3/3) ctg(α) = -3 / √3 ctg(α) = -√3

So, the cotangent of α is -√3.