If θ lies in the second quadrant, which of these products is positive?

In the second quadrant only the sine and its reciprocal are positive: sinθ > 0 and cosecθ > 0, while cosθ, tanθ, cotθ and secθ are all negative. A product is positive only when both factors carry the same sign, and cosθ·cotθ is the only pairing of two negatives here. Each of the other three multiplies a positive by a negative. Check at θ = 130°: cos130°·cot130° = +0.539.