We first need to analyze them individually,
[tex]\begin{gathered} \text{For }\sin \theta<0 \\ \text{Therefore, }\theta\text{ lies in the third and fourth quadrant } \end{gathered}[/tex][tex]\begin{gathered} \text{For sec}\theta>0 \\ \text{Therefore, }\theta\text{ lies in the first and fourth quadrant} \end{gathered}[/tex]The two conditions apply only to the fourth quadrant.
Therefore, the angle lies in the fourth quadrant IV
