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

User Tristian
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1 Answer

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\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.
User Grig
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