Question

2cos x -1>0 решите пожалуйста!!!!!

Answer 1

Ответ:

Решим относительно

x

.

5

π

3

+

2

π

n

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x

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7

π

3

+

2

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для всех целых

n

Нажмите для просмотра шагов...

image of graph

Объяснение:

сори писать с верху в низ

Answer 2

Solving 2cos(x) - 1 > 0

To solve the inequality 2cos(x) - 1 > 0, we need to find the values of x that satisfy this inequality.

Step 1: Find the Critical Points The critical points occur where 2cos(x) - 1 equals 0. This happens when cos(x) = 1/2.

Step 2: Solve for x Using the fact that cos(x) = 1/2 for specific values of x, we can find the solutions for the inequality.

Step 3: Final Solution The final solution will be in the form of intervals for x that satisfy the given inequality.

Let's proceed with the solution based on the critical points and the values of x that satisfy the inequality.

Solution Process

1. Finding Critical Points - The critical points occur where 2cos(x) - 1 equals 0, i.e., where cos(x) = 1/2. - This happens at x = π/3 + 2nπ and x = 5π/3 + 2nπ, where n is an integer.

2. Solving for x - We need to find the intervals where 2cos(x) - 1 > 0, which occurs when cos(x) > 1/2. - This gives us the solution x ∈ (-π/3 + 2nπ, π/3 + 2nπ) U (π/3 + 2nπ, 5π/3 + 2nπ), where n is an integer.

Final Solution

The solution to the inequality 2cos(x) - 1 > 0 is: x ∈ (-π/3 + 2nπ, π/3 + 2nπ) U (π/3 + 2nπ, 5π/3 + 2nπ), where n is an integer.