We need to find the values for theta (0 ≤ theta ≤ 2pi) given the next equation:
[tex]4cosθ+1=2cosθ[/tex]
Let us solve theta:
[tex]\begin{gathered} 4cosθ-2cosθ=-1 \\ 2cosθ=-1 \\ cosθ=\frac{1}{2} \\ θ=\cos^{-1}(-\frac{1}{2}) \\ θ=120\text{ degrees} \end{gathered}[/tex]
Now, we need to convert 120 degrees to radians:
We have that the interval is 2π = 360 degrees.
Hence, 2*120 = 240 degrees is still on the interval.
Convert 240 degrees to radians:
[tex]\frac{240}{180}\ast\pi=\frac{4}{3}\pi[/tex]
Therefore, the result is (2π/3, 4π/3)
The correct answer is the first option.
