Question

Determine which quadrant in which theta lies

Answer 1

(1) sin theta >0 , sec theta<0

Answer 2

think of the unit circle where cos is like the "x" coord and sin is like the "y" coord

sin > 0 means y>0 , this occurs in quad 1 and 2

sec = 1/cos ... 1/cos < 0 is same as cos<0 means x<0 , this occurs in quad 2,3

Both conditions occur in quadrant 2

Answer 3

what about (2)cos <0 , cot >0

here x<0 so it must lie in 2 or 3 quadrant

What abt the next part?

Answer 4

yep
cot = 1/tan ... tan > 0 in quad 1 and 3

Answer 5

ohh so 3rd quad

Answer 6

yeah

tan = y/x , tan positive if both x and y have same sign

Answer 7

So if X or Y would have mutuallly different signs then it couldn't be determined right?

Answer 8

@dumbcow