Question

Sin x = - 1/2 cos x = -1/2 cos x = корень 2 /2 cos x = -1; tg x = – 1; tg x = 0; 2cos 3х - 1 = 0; пжжж розвязати рівняння

Answer 1

Ответ:

sinx210

coax120

cosx45

cosx180

tgx135

tgx0

2cos3x-1=0

Answer 2

Let's solve the given equations step by step:

1. Solve sin x = -1/2: The solutions for sin x = -1/2 are x = 7π/6 + 2πn and x = 11π/6 + 2πn, where n is an integer.

2. Solve cos x = -1/2: The solutions for cos x = -1/2 are x = 2π/3 + 2πn and x = 4π/3 + 2πn, where n is an integer.

3. Solve cos x = √2/2: The solutions for cos x = √2/2 are x = π/4 + 2πn and x = 7π/4 + 2πn, where n is an integer.

4. Solve cos x = -1: The solution for cos x = -1 is x = π + 2πn, where n is an integer.

5. Solve tan x = -1: The solution for tan x = -1 is x = 3π/4 + πn, where n is an integer.

6. Solve tan x = 0: The solution for tan x = 0 is x = 0 + πn, where n is an integer.

7. Solve 2cos(3x) - 1 = 0: 2cos(3x) - 1 = 0 2cos(3x) = 1 cos(3x) = 1/2

The solutions for cos(3x) = 1/2 are 3x = π/3 + 2πn and 3x = 5π/3 + 2πn, where n is an integer. Now divide both sides by 3:

x = π/9 + 2πn/3 and x = 5π/9 + 2πn/3, where n is an integer.

These are the solutions to the given equations. Remember that n can be any integer, which means there are infinitely many solutions for each equation.