What are all solutions to the equation 2 cos Θ = 1 for 0 ≤ Θ ≤ 2? Round to the nearest hundredth.
To solve the equation 2 cos Θ = 1, we first isolate cos Θ:
2 cos Θ = 1
cos Θ = 1/2
Now, we know that the cosine of 60 degrees (π/3 radians) is equal to 1/2. Therefore, the solutions to the equation within the given interval are:
Θ = π/3 ≈ 1.05 radians
Θ = 2π - π/3 = 5π/3 ≈ 5.24 radians
Therefore, the solutions to the equation 2 cos Θ = 1 for 0 ≤ Θ ≤ 2 are approximately 1.05 radians and 5.24 radians.