Answer:
x = 5π/3
Stop-by-step explanation:
We are given the equation:
2cos(x) + 1 = 0
Subtracting 1 from both sides, we get:
2cos(x) = -1
Dividing by 2, we get:
cos(x) = -1/2
We know that the cosine function is negative in the second and third quadrants of the unit circle. In the second quadrant, the reference angle for which the cosine is 1/2 is π/3, and in the third quadrant, the reference angle is also π/3. Therefore, the solutions for x are:
x = π + π/3 = 4π/3 or x = 2π - π/3 = 5π/3
Since the given range is 0 ≤ x ≤ 2π, the only solution in that range is:
x = 5π/3
Therefore, the solution of the equation 2cos(x) + 1 = 0 in the given range is x = 5π/3.