Find tanθ exactly if sinθ=-9/41, and θ is in the fourth quadrant

Keep in mind that, in the IV quadrant, sine or the y-coordinate is negative, and the cosine or x-coordinate is positive, whilst the hypotenuse or radius, is just a distance unit and is never negative.

now, we know the angle is in the IV quadrant, therefore the opposite side or "y" is negative, thus