Final answer:
The solutions to the equation 2sin(θ) - 1 = 0 in the interval [0,2π) are θ = π/6 and θ = 5π/6.
Step-by-step explanation:
To find all solutions of the equation 2sin(θ) - 1 = 0 in the interval [0,2π), we first isolate sin(θ) by adding 1 to both sides and then dividing by 2. This gives us sin(θ) = 1/2. Next, we need to determine the angles within the given interval for which the sine value is 1/2.
There are two angles between 0 and 2π (0 and 360 degrees) where the sine function has a value of 1/2: these are θ = π/6 (or 30°) and θ = 5π/6 (or 150°). Therefore, the solutions to the equation in the given interval are θ = π/6 and θ = 5π/6.