Given #sectheta>0# and #cottheta<0#, which quadrant does #theta# lie?

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Answer 1 · 2017-01-07T19:45:46

#theta# lies in the Fourth Quadrant.

#sec theta > 0 rArr theta in Q_I uu Q_(IV)#

#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.