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

2 sin θ cos θ + cos θ = 0

1 answer

We can factor out cos θ from the left-hand side of the equation:

2 sin θ cos θ + cos θ = cos θ (2 sin θ + 1) = 0

This means that either cos θ = 0 or 2 sin θ + 1 = 0.

If cos θ = 0, then θ must be either π/2 or 3π/2.

If 2 sin θ + 1 = 0, then sin θ = -1/2. There are two values of θ between 0 and 2π that satisfy this condition: θ = 7π/6 and θ = 11π/6.

Therefore, the values of θ that satisfy the equation are θ = π/2, 3π/2, 7π/6, and 11π/6.