Решение
<span>sin α = -4/5 и α ∈(3/2π;2π)
</span>sin²(α/2) = (1 - cosα)/2
cosα = √(1 - sin²α) = √(1 - (-4/5)²) = √9/25 = 3/5
sin²(α/2) = (1 - 3/5)/2
<span>sin²(α/2) = (2/5) : 2
</span><span>sin²(α/2) = 1/5
</span>sin(α/2) = √(1/5); sin(α/2) = √5/5
sin(α/2) = - √(1/5); <span>sin(α/2) = - </span>√5/5
5^2 * 80 * 3^10 = 25*80*3^10 = 2000*3^10 = 2000*59049 = 118098000
BH-высота
cosA=2/5
sinA=√(1=cos²A)=√(1-4/25)=√(21/25)=√21/5
AB=BH/sinA=2√21:√21/5=2√21*5/√21=10
F(x) = log_(0,2) (7x - x^2)
Логарифм нуля и отрицательных чисел не существует, значит:
7x - x^2 > 0
x*(7 - x) > 0
x*(x - 7) < 0
x1 = 0
x2 = 7
+ - +
---------------------------------------------------------->
0 7 x
x ∈ (0 ; 7)