Відповіді АЛГЕБРА: 16.29

16.29

1) cos(2x – π4) = 22

2x – π4 = ± π4 + 2πn, n є z;

2x = π4 ± π4 + 2πn, n є z;

x = π8 ± π8 + πn, n є z;

Найм. дод. корінь (x = π8 + π8 = 2π8 = π4);

2) sin(x2 + π6) = 12

x2 + π6 = (–1)ⁿ π6 + πn, n є z;

x2 = (–1)ⁿ π6 – π6 + πn;

x = (–1)ⁿ π3 – π3 + 2πn, n є z;

n = 0; x = π3 – π3 + 2π • 0 = 0;

n = 1; x = –π3 – π3 + 2π = 2π – 2π3 = 4π3