Question

Cos x > √2/2 косинус x, больше корня из двух делённое на два

Answer 1

Ответ:==========

Пошаговое объяснение:

во вложении

Answer 2

To solve the inequality cos(x) > √2/2, we need to determine the range of values for x that satisfy the inequality.

First, let's find the values of x where cos(x) equals √2/2. We know that cos(π/4) = √2/2, so one solution is x = π/4. Additionally, since cosine is a periodic function with a period of 2π, we can find other solutions by adding multiples of the period. Therefore, we have x = π/4 + 2πn, where n is an integer.

Now, let's analyze the behavior of cos(x) and √2/2 in the interval (0, 2π).

• For values of x in the interval (0, π/4), cos(x) > √2/2.
• For x = π/4, cos(x) = √2/2.
• For values of x in the interval (π/4, π/2), cos(x) < √2/2.
• For x = π/2, cos(x) = 0, which is less than √2/2.

Since cosine is a continuous function, we can conclude that cos(x) > √2/2 for x in the intervals (0, π/4) and (7π/4, 2π), as well as for x = π/4 + 2πn, where n is an integer.

In interval notation, the solution to the inequality cos(x) > √2/2 is:

x ∈ (0, π/4) ∪ (7π/4, 2π) ∪ {π/4 + 2πn | n is an integer}