Use the special triangles on the unit circle to determine θ in degrees when sinθ=3√2 . (1 point) Responses 45° 45° 30° 30° 90° 90° 60°
The special triangles on the unit circle are the 45-45-90 triangle and the 30-60-90 triangle.
In the 45-45-90 triangle, the lengths of the sides are in the ratio 1:1:√2. Since sinθ = opposite/hypotenuse, we set up the equation sinθ = 3√2/1. Since the opposite side in this triangle has length 1, we can see that sinθ = 1/√2. Therefore, θ must be 45°.
In the 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. In this triangle, sinθ = opposite/hypotenuse. Since the opposite side in this triangle is √3, we can see that sinθ = √3/2. Therefore, θ must be 60°.
So, the correct response is 60°.