sin(theta)<0 and sec(theta)>0, what quadrant do they belong?

Question

Given sinΘ≤0 and secΘ≥0, state the quadrant in which Θ resides.

Answer 1

To follow on Mark's train of thought, he's identified the where the respective trigonometric functions are negative. To put it all together, considering the question, we're looking for where their negative quadrant overlaps. This is in quadrant III (QIII), therefore QIII answers your question.

Answer 2

The sine is negative in QIII and QIV.

The secant (the inverse of the cosine) is negative in QII and QIII.