ANSWER
D. Quadrant IV
EXPLANATION
[tex]\sin\theta \:<\:0[/tex]
means the sine ratio is negative.
[tex]\tan\theta \:<\:0[/tex]
also means the tangent ratio is negative.
The only trigonometric ratio that is position in the fourth quadrant is the cosine ratio and its reciprocal, the secant ratio.
The tangent ratio and the sine ratio, with their reciprocals as well are negative in the fourth quadrant.
Hence the angle, [tex]\theta[/tex] is in the fourth quadrant.
The correct answer is D.
