Question

Cos X = (в корне 3)/2, X€ [0;2п]

Answer 1

Ответ:

Пошаговое объяснение:

х=± П/6+2пk, k-целое

Только П/6+2пk  входит в промежуток 0;2п]  

отрицательный в него не попадает, так как там идет уже промежуток от [-2П;0]

Answer 2

To find the solutions for the equation cos(x) = (√3)/2 in the given interval [0, 2π], we need to determine the values of x that satisfy this equation.

We know that the cosine function has a value of (√3)/2 at two specific angles: π/6 and 11π/6 (among others), due to its periodic nature. So, we can start by finding these angles within the given interval.

First, let's find the angle within [0, 2π] that has a cosine value of (√3)/2.

cos(x) = (√3)/2

To find the angle x, we can take the inverse cosine (also known as arccos) of both sides of the equation:

x = arccos((√3)/2)

Using the arccos function, we find:

x = π/6

Now, let's add 2π to x to find the second angle within the given interval:

x = π/6 + 2π

Simplifying this expression:

x = π/6 + 12π/6

x = 13π/6

Therefore, the solutions for the equation cos(x) = (√3)/2 in the interval [0, 2π] are x = π/6 and x = 13π/6.