Если sin α = -4/5 и α ∈(3/2π; 2π),то величина sin α/2 равна ? !

Решение
sin α = -4/5 и α ∈(3/2π;2π)
sin²(α/2) = (1 - cosα)/2
cosα = √(1 - sin²α) = √(1 - (-4/5)²) = √9/25 = 3/5
sin²(α/2) = (1 - 3/5)/2
sin²(α/2) = (2/5) : 2
sin²(α/2) = 1/5
sin(α/2) = √(1/5); sin(α/2) = √5/5
sin(α/2) = - √(1/5); sin(α/2) = - √5/5