Question

What quadrant does sec(theta)>0 and cot(theta)<0 lie in

Answer 1

`\sec\theta=\frac1{\cos\theta}>0\implies\cos\theta>0`

This happens in the first and fourth quadrants.

Since cosine is positive,


`\cot\theta=(\cos\theta)/(\sin\theta)<0\implies\sin\theta<0`

and this happens in the third and fourth quadrants.

This means both conditions can only occur in the fourth quadrant.