§ 28: 28.5

28.5 Розв’яжіть рівняння:

1) sin(x – π6) = 22; x – π6 = (–1)ⁿarcsin22 + πn, n ∈ Z;

x = (–1)ⁿπ4 + π6 + πn, n ∈ Z;

2) sin(π6 + 1) = –1; x3 + 1 = – π2 + 2πn, n ∈ Z; x3 = –π2 – 1 + 2πn, n ∈ Z;

x = –3π2 – 3 + 6πn, n ∈ Z;

3) sin(π12 – 3x) = 12; sin(3x – π12) = –22;

3x – π12 = (–1)ⁿarcsin(–22) + πn, n ∈ Z; 3x = (–1)ⁿ⁺³π4 + π12 + πn,n ∈ Z;

x = (–1)ⁿ⁺¹π12 + π36 + πn3, n ∈ Z;