If $Cot > theta$ , $sin<theta$ what quadrant does theta lie?

Question

4203 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-21T09:10:42

3rd quadrant

By definition

$sintheta="Perpendicular (P)"/ "Hypotenuse(H)"$

$cottheta=" Base(B)"/ "Perpendicular(P)"$

$"Hypotenuse is always">0$

So $sintheta<0," " "when (P)" <0->"theta in 3rd or 4th quadrant"$

Again
$cot theta>0," " "When B and P both" > "or" <0->"theta in 1st or 3rd quadrant"$
In 1st quadrant B and P both >0
In 3rd quadrant B and P both <0

Hence the two given conditions will be satisfied if $theta$ is in 3rd quadrant

If Cot > thetaCot > theta, sin<thetasin<theta what quadrant does theta lie?