Considere as expressões:

$$\begin{array}{rlr}& \text{(I) }\frac{\mathrm{sen}30^{\circ }\cdot \cos 150^{\circ }}{\mathrm{tg}210^{\circ }}& \text{(II) }\frac{\mathrm{cotg}50^{\circ }\cdot \mathrm{sen}93^{\circ }}{\mathrm{tg}181^{\circ }}\\ & \text{(III) }\frac{\cos x\cdot \mathrm{cossec}x}{\sec x\cdot \mathrm{cotg}x},x\in ]\frac{3\pi }{2},2\pi [& \text{(IV) }\frac{\mathrm{sen}x\cdot \mathrm{tg}x}{\mathrm{cossec}x},x\in ]\frac{\pi }{2},\pi [\end{array}$$

Têm valor sempre negativo: