Найдите корни уравнения sinФи=-1 принадлежащие промежутку Фи[0; 4pi]

Sin Фи = - 1

Фи = - π/2 + 2πn, n∈Z

Фи∈[0; 4π]

0≤ - π/2+2πn ≤ 4π

π/2 ≤ 2πn ≤ 4π + π/2

π/2 ≤ 2πn ≤ 9π/2

π ≤ n ≤ 9π

2*2π 2*2π

1/4 ≤ n ≤ 9/4

0.25 ≤ n ≤ 2.25

n=1 Фи = - π/2 + 2π = 3π/2

n=2 Фи = - π/2 + 2π*2 = - π/2 + 4π = 7π/2

Ответ: 3π/2; 7π/2.