Question

In which quadrant does angle theta lie if csc theta <0 and cot theta<0?

Answer 1

Answer:

$\csc( \alpha ) < 0$

=>

$\frac{1}{ \sin( \alpha ) } < 0$

=>

$\sin( \alpha ) < 0$

we also have:

$\cot( \alpha ) < 0$

$= > \frac{ \cos( \alpha ) }{ \sin( \alpha ) } < 0$

but sin < 0 (proven)

$= > \cos( \alpha ) < 0$

=> angle theta is in the 3rd quadrant