§ 27: 27.5 (1-2)

27.5 Розв’яжіть рівняння:

1) cos(x + π6) = 22; x + π6 = ± arccos22 + 2πn, n ∈ Z; x + π6 = ± π4 + 2πn, n ∈ Z; x = ± π4 – π6 + 2πn, n ∈ Z;

2) cos(x6 – 2) = –1; x6 – 2 = π + 2πn, n ∈ Z; x6 = π + 2 + 2πn, n ∈ Z;

x = 6π + 12 + 12πn, n ∈ Z;

3) 2cos(π8 – 3x) + 1 = 0; 2cos(3x – π8) = –1; cos(3x – π8) = –12; 3x – π8 = ±arccos(–12) + 2πn, n ∈ Z; 3x – π8 = ±(π – arccos12) + 2πn, n ∈ Z;

3x – π8 = ±(π – π3) + 2πn, n ∈ Z; 3x – π8 = ± 2π3 + 2πn, n ∈ Z;

3x = ± 2π3 + π8 + 2πn, n ∈ Z; x = ± 2π9 +π24 + 2πn3, n ∈ Z.