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

Question

2 sin θ cos θ + Start Root 3 End Root cos θ = 0

Answer 1

The equation given is:

2 sin θ cos θ + √3 cos θ = 0

Factoring out cos θ, we get:

cos θ(2 sin θ + √3) = 0

This equation will be satisfied when either cos θ = 0 or (2 sin θ + √3) = 0.

For cos θ = 0, values of θ that satisfy this condition are θ = π/2 and θ = 3π/2.

For (2 sin θ + √3) = 0, solving for θ gives θ = π/6 and θ = 5π/6.

Therefore, the values for θ (0 ≤ θ ≤ 2π) that satisfy the equation are θ = π/2, π/6, 3π/2, and 5π/6.