Given $sec θ > 0$ $sectheta>0$ and $cot θ < 0$ $cottheta<0$ , which quadrant does $θ$ $theta$ lie?

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Answer 1 · 2017-01-07T19:45:46

$θ$ $theta$ lies in the Fourth Quadrant.

$sec θ > 0 \Rightarrow θ \in Q_{I} \cup Q_{I V}$ $sec theta > 0 rArr theta in Q_I uu Q_(IV)$

$cot θ < 0 \Rightarrow θ \in Q_{I I} \cup Q_{I V}$ $cot theta < 0 rArr theta in Q_(II) uu Q_(IV)$

$:. sec theta gt 0 & cottheta lt 0$

$rArr theta in [Q_I uu Q_(IV)] nn [Q_(II) uu Q_(IV)]$

But $[AuuB]nn[CuuB]=[AnnC]uuB$

$:. theta in [Q_InnQ_(II)]uuQ_(IV)=Q_(IV)$

Hence, $theta$ lies in the Fourth Quadrant.

Given sectheta>0secθ>0sectheta>0 and cottheta<0cotθ<0cottheta<0, which quadrant does thetaθtheta lie?