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

Question

(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 $\sin \theta =3\sqrt{2}$.