Question

in which quadrant would θ be if sinθ = -√3/2 and tanθ < 0? use a digit for your response rather than a roman numeral. (1 point) quadrant check answer remaining attempts : 3

Explanation:

Step1: Analyze sine sign

$\sin\theta = -\frac{\sqrt{3}}{2} < 0$, so $\theta$ is in quadrant 3 or 4 (since sine is negative in those quadrants).

Step2: Analyze tangent sign

$\tan\theta < 0$, which means sine and cosine have opposite signs (as $\tan\theta=\frac{\sin\theta}{\cos\theta}$). Since $\sin\theta$ is negative, $\cos\theta$ must be positive. Cosine is positive in quadrant 1 or 4.

Step3: Find common quadrant

The common quadrant from step1 (3 or 4) and step2 (1 or 4) is quadrant 4.

Answer:

4