§ 27: 27.3 (1-3)

27.3 Розв’яжіть рівняння:

1) cos3x = –12; 3x = ± arccos(–12) + 2πn, n ∈ Z;

3x = ± (π – arccos12) + 2πn, n ∈ Z; 3x = ±(π – π3) + 2πn, n ∈ Z;

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

2) cos56x = 32; 56x = ± arccos32 + 2πn, n ∈ Z; 56x = ± π6 + 2πn, n ∈ Z; x = ± π5 + 12πn5, n ∈ Z;

3) cos6x = 1; 6x = 2πn, n ∈ Z; x = 2πn3, n ∈ Z;π6 + 2πn, n ∈ Z;

4) cos2πn3 = 0; 2πn3 = π2 + 2πn, n ∈ Z; x = 34 + 3n2, n ∈ Z;

5) cos9x = –15; 9x = ± arccos(–15) + 2πn, n ∈ Z;

9x = ± (π – arccos15) + 2πn, n ∈ Z; x = ± (π9 – 19 arccos15) + 2πn, n ∈ Z;

6) cos(–x3) = 33; cosx3 = 33; x3 = ±arccos33 + 2πn, n ∈ Z;

x = ±3arccos33 + 6πn, n ∈ Z.