Тригонометрические уравнения

Решите уравнение: sin^2(x) - 3sin(x) + 2 = 0

• x = π/2 + 2kπ, k ∈ Z

• x = π/4 + 2kπ, k ∈ Z

• x = 0 + 2kπ, k ∈ Z

• x = π + 2kπ, k ∈ Z

Найдите все решения: cos^2(x) - 4cos(x) + 3 = 0

• x = π/4 + kπ, k ∈ Z

• x = 3π/2 + 2kπ, k ∈ Z

• x = 2kπ, k ∈ Z

• x = π/3 + 2kπ, k ∈ Z

Решите уравнение: 2sin^2(x) - sin(x) - 1 = 0

• x = π/3 + 2kπ

• x = 7π/6 + 2kπ, x = 11π/6 + 2kπ, x = π/2 + 2kπ

• x = 3π/2 + 2kπ

• x = 5π/6 + 2kπ

Найдите x: 3cos^2(x) - 5cos(x) + 2 = 0

• x = arccos(1/2) + 2kπ

• x = arccos(2/3) + 2kπ, x = -arccos(2/3) + 2kπ, x = 2kπ (k ∈ ℤ)

• x = 3kπ (k ∈ ℤ)

• x = arccos(-1/2) + 2kπ

Решите уравнение: sin^2(x) + sin(x) - 2 = 0

• x = -π/2 + 2kπ, k ∈ Z

• x = π/2 + 2kπ, k ∈ Z

• x = π + 2kπ, k ∈ Z

• x = 0 + 2kπ, k ∈ Z

Найдите все решения: 4sin^2(x) - 4sin(x) + 1 = 0

• x = 0 + 2kπ

• x = 3π/4 + 2kπ

• x = π/6 + 2kπ, x = 5π/6 + 2kπ, k ∈ Z

• x = π/4 + 2kπ

Решите уравнение: cos^2(x) + 2cos(x) - 3 = 0

• x = π/2 + 2kπ, k ∈ Z

• x = π + 2kπ, k ∈ Z

• x = 2kπ, k ∈ Z

• x = 3π/2 + 2kπ, k ∈ Z

Найдите x: 5sin^2(x) - 5sin(x) + 1 = 0

• x = arcsin(0) + 2kπ

• x = arcsin(-1) + 2kπ

• x = arcsin(1) + 2kπ

• x = arcsin((5 + sqrt(5))/10) + 2kπ, x = arcsin((5 - sqrt(5))/10) + 2kπ, k ∈ Z

Решите уравнение: 2cos^2(x) - 3cos(x) + 1 = 0

• x = π/2 + 2kπ

• x = 2π/3 + 2kπ

• x = 4π/3 + 2kπ

• x = 0 + 2kπ, x = π/3 + 2kπ, x = 5π/3 + 2kπ, k ∈ Z

Найдите все решения: sin^2(x) - sin(x) = 0

• x = nπ/2, x = 3π/2 + 2kπ, x = π + kπ, where n, k are integers.

• x = nπ, x = π/2 + 2kπ, where n, k are integers.