Solve the equation 2 cos (x) + 1 = 0,0< x<2π

Answer 1

To solve the equation 2*cos(x) + 1 = 0, within the given interval 0 < x < 2π, we follow these steps:

Subtract 1 from both sides:
2*cos(x) = -1

Divide by 2:
cos(x) = -1/2

Using the unit circle or reference angles on the unit circle, we find that the cosine function is equal to -1/2 when the angle is 2π/3 or 4π/3.

So, the solutions to the equation 2*cos(x) + 1 = 0, within the interval 0 < x < 2π, are x = 2π/3 and x = 4π/3.