Wayground logo

Free Printable Worksheets

Font size

S
M
L
XL
Worksheets

Решение тригонометрических уравнений

Total questions: 10

Worksheet time: 10mins

Name
Class
Date
1.

Решите уравнение: sin(x) = 0.5

a)

x = 3π/4 + 2kπ, k ∈ Z

b)

x = 7π/6 + 2kπ, k ∈ Z

c)

x = π/6 + 2kπ, x = 5π/6 + 2kπ, k ∈ Z

d)

x = π/4 + 2kπ, k ∈ Z

2.

Найдите все решения уравнения: cos(x) = -1

a)

x = (2n - 1)π, n ∈ Z

b)

x = (2n + 1)π, n ∈ Z

c)

x = 2nπ, n ∈ Z

d)

x = (n + 1)π/2, n ∈ Z

3.

Решите уравнение: tan(x) = √3

a)

x = π/4 + kπ, k ∈ Z

b)

x = π/2 + kπ, k ∈ Z

c)

x = π/3 + kπ, k ∈ Z

d)

x = π/6 + kπ, k ∈ Z

4.

Определите все решения: sin(2x) = 1

a)

x = π/3 + kπ, k ∈ Z

b)

x = π/4 + kπ, k ∈ Z

c)

x = π/2 + kπ, k ∈ Z

d)

x = π/6 + kπ, k ∈ Z

5.

Решите уравнение: cos(2x) = 0

a)

x = (2n - 1)π/6, n ∈ Z

b)

x = nπ/2, n ∈ Z

c)

x = (2n + 1)π/4, n ∈ Z

d)

x = (2n)π/3, n ∈ Z

6.

Найдите x, если: sin(x) + sin(2x) = 0

a)

x = nπ, x = (2n+1)π/3, where n is an integer.

b)

x = nπ/3, x = (2n+1)π/2, where n is an integer.

c)

x = nπ/6, x = (2n+1)π/2, where n is an integer.

d)

x = nπ/2, x = (2n+1)π/4, where n is an integer.

7.

Решите уравнение: 2cos^2(x) - 1 = 0

a)

x = π/4 + 2kπ, 3π/4 + 2kπ, k ∈ Z

b)

x = π/6 + 2kπ, 5π/6 + 2kπ, k ∈ Z

c)

x = π/3 + 2kπ, 2π/3 + 2kπ, k ∈ Z

d)

x = 0 + kπ, π + kπ, k ∈ Z

8.

Определите все решения: tan(x) + 1 = 0

a)

x = π/4 + kπ, k ∈ Z

b)

x = 0 + kπ, k ∈ Z

c)

x = -π/4 + kπ, k ∈ Z

d)

x = -3π/4 + kπ, k ∈ Z

9.

Решите уравнение: sin(x) * cos(x) = 0.5

a)

x = π/2 + kπ, k ∈ Z

b)

x = π/4 + kπ, k ∈ Z

c)

x = π/6 + kπ, k ∈ Z

d)

x = π/3 + kπ, k ∈ Z

10.

Найдите все решения: 3sin(x) - 2 = 0

a)

x = arcsin(3/2) + 2kπ, k ∈ Z

b)

x = arcsin(2/3) + 2kπ, x = π - arcsin(2/3) + 2kπ, k ∈ Z

c)

x = arcsin(1/3) + 2kπ, k ∈ Z

d)

x = 2arcsin(2/3) + 2kπ, k ∈ Z