Question

Решите уравнения!(Триногеметрические уравнения)

Answer 1

Решение
1) sinx = - 1/2
x = (-1)^n *arcsin(-1/2) + πn, n ∈ Z
x = (-1)^(n+1) *arcsin(1/2) + πn, n ∈ Z
x = (-1)^(n+1) *(π/6) + πn, n ∈ Z
2)  3tgx = 0
tgx = 0
x = πk, k ∈ Z
3)  cos4x = 0
4x = π/2 + πn, n ∈ Z
x = π/8 + (πn)/4, n ∈ Z
4)  cos(3x - π/6) = - 1
3x - π/6 = π + 2πk, k ∈ Z
3x = π/6 + π + 2πk, k ∈ Z
3x = 7π/6 + 2πk, k ∈ Z
x = 7π/18 + (2πk)/3, k ∈ Z