Задача 76028 ...

632f635587d19127bff140f0

2/27/2024 8:11:00 PM

Решите уравнение: 6 sin^(2)x+5cos x-7=0 , Ответы: (-1)^(k)arcos 1/3+πk, k ∈ Z, (-1)^(n)π/3+πn, n ∈ Z. arcos 1/3+2πk, k ∈ Z, π/3+2πn, n ∈ Z. ± arcos1/3+2πk, k ∈ Z, ± π/3+2πn, n ∈ Z. ± arcos2/3+2πk, k ∈ Z, ± π/6+2πn, n ∈ Z.

626fab9a354ab65fb2f43abb

2/27/2024 8:37:59 PM

★

6 sin^2 x + 5cos x – 7 = 0
6(1 - cos^2 x) + 5cos x – 7 = 0
6 - 6cos^2 x + 5cos x – 7 = 0
6cos^2 x - 5cos x + 1 = 0
D = (-5)^2 - 4*6*1 = 25 - 24 = 1 = 1^2
cos x1 = (5 - 1)/12 = 4/12 = 1/3
[b]x1 = ± arccos(1/3) + 2π*k, k ∈ Z[/b]
cos x2 = (5 + 1)/12 = 6/12 = 1/2
[b]x2 = ± π/3 + 2π*n, n ∈ Z[/b]