Question

What values for theta (0 ≤ theta ≤ 2pi) satisfy the equation?see image

Answer 1

We need to find the values for theta (0 ≤ theta ≤ 2pi) given the next equation:

`4cosθ+1=2cosθ`

Let us solve theta:

`\begin{gathered} 4cosθ-2cosθ=-1 \\ 2cosθ=-1 \\ cosθ=(1)/(2) \\ θ=\cos^(-1)(-(1)/(2)) \\ θ=120\text{ degrees} \end{gathered}`

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:

`(240)/(180)\ast\pi=(4)/(3)\pi`

Therefore, the result is (2π/3, 4π/3)

The correct answer is the first option.