Question

Use the special triangles on the unit circle to determine θ in degrees when sinθ=3√2 .

(1 point)
Responses

60°
60°

45°
45°

90°
90°

30°

Answer 1

The sine function, \( \sin \theta \), ranges from -1 to 1 for real angles. Given \( \sin \theta = 3\sqrt{2} \), we can evaluate whether this condition is possible.

1. The maximum value of sine is 1. Thus, \( 3\sqrt{2} \) is approximately \( 3 \times 1.414 \approx 4.242 \), which is greater than 1.
2. Therefore, there are no angles \( \theta \) for which \( \sin \theta = 3\sqrt{2} \).

Since the given value is outside the possible range of the sine function, none of the given responses (60°, 45°, 90°, 30°) are correct. Thus, the proper conclusion is that there are no angles where \( \sin \theta = 3\sqrt{2} \).