Question

Find all solutions to 2sin(θ)=√3 on the interval 0≤θ<2π

Answer 1

Answer:

2sin(3θ) - √3 = 0

Step-by-step explanation:

 sin(3θ) = √3/2

 

3θ = π/3 + 2kπ or 2π/3 + 2kπ, k = 0, ±1, ±2, ±3,...

 

θ = π/9 + 2kπ/3, 2π/9 + 2kπ/3

 

If k = 0, we get θ = π/9, 2π/9

If k = 1, we get θ = 7π/9, 8π/9

If k = 2, we get θ = 13π/9, 14π/9

 

Other values of k give values of θ lying outside of the interval [0, 2π).