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

May 21, 2016

#### Explanation:

By definition

$\sin \theta = \text{Perpendicular (P)"/ "Hypotenuse(H)}$

$\cot \theta = \text{ Base(B)"/ "Perpendicular(P)}$

$\text{Hypotenuse is always} > 0$

So $\sin \theta < 0 , \text{ " "when (P)" <0->"theta in 3rd or 4th quadrant}$

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