Question

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

Answer 1

3rd quadrant

Explanation:

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