In which quadrant would θ be if tanθ=−3–√ and sinθ>0 ?(1 point) Responses Quadrant IV Quadrant IV Quadrant III Quadrant III Quadrant I Quadrant I Quadrant II Quadrant II

Answer 1

To determine the quadrant in which the angle θ lies based on the conditions given, we need to analyze the signs of the trigonometric functions involved.

1. We have \( \tan \theta = -\sqrt{3} \). The tangent function is negative in Quadrants II and IV.
2. We also know that \( \sin \theta > 0 \). The sine function is positive in Quadrants I and II.

Since we need both conditions to be true (tangent negative and sine positive), θ must be in Quadrant II.

Thus, the correct answer is:

Quadrant II