sinθ = 1/2 and cosθ = -√3/2, what is the value of θ?

sinθ = ¹/₂ and cosθ = -√3/2, what is the value of θ?

Answer Details

We can use the fact that sin²θ + cos²θ = 1, to find the value of sinθ or cosθ given the other one. Since sinθ = 1/2, we know that sin²θ + cos²θ = 1 becomes: (1/2)² + cos²θ = 1 Simplifying the equation, we get: 1/4 + cos²θ = 1 cos²θ = 3/4 Taking the square root of both sides, we get: cosθ = ±√3/2 Since we know that cosθ = -√3/2, we can conclude that θ = 150^o (or 5π/6 radians) as this is the angle in the fourth quadrant that has a cosine of -√3/2. Therefore, the answer is option E: 150^o.