WorksheetsРешение тригонометрических уравнений
Total questions: 10
Worksheet time: 10mins
Решите уравнение: sin(x) = 0.5
x = 3π/4 + 2kπ, k ∈ Z
x = 7π/6 + 2kπ, k ∈ Z
x = π/6 + 2kπ, x = 5π/6 + 2kπ, k ∈ Z
x = π/4 + 2kπ, k ∈ Z
Найдите все решения уравнения: cos(x) = -1
x = (2n - 1)π, n ∈ Z
x = (2n + 1)π, n ∈ Z
x = 2nπ, n ∈ Z
x = (n + 1)π/2, n ∈ Z
Решите уравнение: tan(x) = √3
x = π/4 + kπ, k ∈ Z
x = π/2 + kπ, k ∈ Z
x = π/3 + kπ, k ∈ Z
x = π/6 + kπ, k ∈ Z
Определите все решения: sin(2x) = 1
x = π/3 + kπ, k ∈ Z
x = π/4 + kπ, k ∈ Z
x = π/2 + kπ, k ∈ Z
x = π/6 + kπ, k ∈ Z
Решите уравнение: cos(2x) = 0
x = (2n - 1)π/6, n ∈ Z
x = nπ/2, n ∈ Z
x = (2n + 1)π/4, n ∈ Z
x = (2n)π/3, n ∈ Z
Найдите x, если: sin(x) + sin(2x) = 0
x = nπ, x = (2n+1)π/3, where n is an integer.
x = nπ/3, x = (2n+1)π/2, where n is an integer.
x = nπ/6, x = (2n+1)π/2, where n is an integer.
x = nπ/2, x = (2n+1)π/4, where n is an integer.
Решите уравнение: 2cos^2(x) - 1 = 0
x = π/4 + 2kπ, 3π/4 + 2kπ, k ∈ Z
x = π/6 + 2kπ, 5π/6 + 2kπ, k ∈ Z
x = π/3 + 2kπ, 2π/3 + 2kπ, k ∈ Z
x = 0 + kπ, π + kπ, k ∈ Z
Определите все решения: tan(x) + 1 = 0
x = π/4 + kπ, k ∈ Z
x = 0 + kπ, k ∈ Z
x = -π/4 + kπ, k ∈ Z
x = -3π/4 + kπ, k ∈ Z
Решите уравнение: sin(x) * cos(x) = 0.5
x = π/2 + kπ, k ∈ Z
x = π/4 + kπ, k ∈ Z
x = π/6 + kπ, k ∈ Z
x = π/3 + kπ, k ∈ Z
Найдите все решения: 3sin(x) - 2 = 0
x = arcsin(3/2) + 2kπ, k ∈ Z
x = arcsin(2/3) + 2kπ, x = π - arcsin(2/3) + 2kπ, k ∈ Z
x = arcsin(1/3) + 2kπ, k ∈ Z
x = 2arcsin(2/3) + 2kπ, k ∈ Z
