Y a tangent and chord theorem
What is the measure of Qs?

If you draw the circle and divide into 4 quadrants, you can see that the sine is negative, since the quadrant is situated in the negative part of YY', and that the cosine is positive, since the quadrant is situated in the positive part of XX'.
And , and negative divided by positive gives a negative answer, which means that the tangent is negative on the quadrant IV.
Hope this helps :)