Question

If sinθ>0 and tangθ<0, explain how to find the Quadrant in which θ lies.

Answer 1

Use the following quadrant map, which spells CAST in counter-clockwise direction:

S|A
----
T|C

This means that Cosine is positive in the fourth quadrant, All three are positive in the first quadrant, Sine is positive in the second quadrant, and Tangent is positive in the third quadrant. Functions not mentioned are negative in the respective quadrants.

So if sinθ>0 and tanθ<0, it cannot be in the first quadrant. The only other quadrant where sinθ>0 is the second, where tanθ<0.