Question

Решите уравнение: -2cosx=1

Answer 1

$-2cosx=1 \\ cosx=-\frac{1}{2} \\x=\pm \frac{2\pi}{3}+2\pi*n,\ n \in Z$

Answer 2

Решение во вложении.
Надеюсь помог)

Answer 3

To solve the equation -2cos(x) = 1, follow these steps:

Step 1: Isolate the cosine term. Divide both sides of the equation by -2: cos(x) = -1/2

Step 2: Find the solutions in the given range. The solutions for cos(x) = -1/2 lie in the interval [0, 2π], where cosine is negative. This interval covers one full cycle of the cosine function.

Step 3: Find the angles where cos(x) equals -1/2. To find the angles where cos(x) equals -1/2, you can use the inverse cosine function (also known as arccos or cos^-1). In degrees, this would be:

x = arccos(-1/2)

Using a calculator, you can find the principal value of arccos(-1/2):

x ≈ 120°

Step 4: Find additional solutions (if any). Since the cosine function is periodic with a period of 2π, you can add integer multiples of the period to the principal value to find other solutions:

x ≈ 120° + 360°k (where k is an integer)

The values of k can be 0, 1, 2, 3, ... and so on, or negative values -1, -2, -3, ... to cover all solutions in the interval [0, 2π].

So the complete set of solutions is:

x ≈ 120°, 480°, 840°, ... (in degrees) or x ≈ π/3, 4π/3, 7π/3, ... (in radians)