Determine the quadrant where θ lies given that sinθ < 0 and tanθ > 0.IIIIIIIV

The answer to this question is quadrant III. Since
sinθ = y/r and tanθ = y/x, we have, in quadrant III, x, y negative.

sinθ < 0 (r always positive) but tanθ > 0 (negative divided by negative is positive).