Final answer:
The values of θ that satisfy the equation 4cos² θ - 2cos θ = 1 in the range (0 ≤ θ ≤ 360°) are 120°, 240°, 300°, and 360°.
Step-by-step explanation:
To find the values of θ in the range (0 ≤ θ ≤ 360°) that satisfy the equation 4cos² θ - 2cos θ = 1, we can rearrange the equation to form a quadratic equation:
4cos² θ - 2cos θ - 1 = 0.
We can solve this quadratic equation by factoring or using the quadratic formula. In this case, factoring is the most efficient method. The factored form of the equation can be written as (2cosθ + 1)(2cosθ - 1) = 0. Setting each factor equal to zero, we get 2cosθ + 1 = 0 and 2cosθ - 1 = 0.
Solving these equations gives us cosθ = -1/2 and cosθ = 1/2. We can then find the values of θ using the inverse cosine function (cos¹). The values of θ that satisfy these equations are θ = 120°, 240°, 300°, and 360°.