What values for θ (0 ≤ θ ≤ 2π) satisfy the equation?

Question

3sinθ = sinθ – 1

Answer 1

To solve this equation, first, let's simplify it:

3sinθ = sinθ - 1

Subtract sinθ from both sides:

3sinθ - sinθ = -1
2sinθ = -1

Divide by 2:

sinθ = -1/2

Now, we know that sin(π/6) = 1/2 and sin(5π/6) = -1/2. Therefore, the values for θ that satisfy the equation are:

θ = π/6 and θ = 5π/6.