Question

Determine the quadrant when the terminal side of the angle lies according to the following condition: cot (t) < 0, cos (t) < 0

Answer 1

Remember a simple but effective mnemonic "ALL SILVER TEA CUPS". For angles lying in the 1st quadrant, all trigonometric ratios will give positive value or value>0 , for angles lying in 2nd quadrant only sin of theta for theta lying in 2nd quadrant will give +ve value. Similarly you have +ve values of cos theta in 3rd quadrant and that of tan theta in 4th quadrant for theta lying in the respective quadrants.

Answer 2

The inverses will follow the same rule. Sec will follow cos, cosec will follow sin and cot will follow tan respectively.

Answer 3

So then would it be quad II?

Answer 4

Yes, you got it correct.

Answer 5

Well done.

Answer 6

I have one more could you help? sin (t) < 0, csc (t) > 0
Sin(t) < 0 would be in quad 3 or 4, right?

Answer 7

Yeah.

Answer 8

I'm confused about the csc (t) > 0.

Answer 9

It should follow sin. Are you sure the question is correct?

Answer 10

Yeah, that's what it says

Answer 11

I think the question is wrong, because if you take any value of a particular angle and sin of that angle is less than zero, then cosec of that will also be less than zero since inverse of a negative number is a negative number, right?

Answer 12

Or you could say that no value of theta satisfies the given conditions.

Answer 13

It would be better if you would check the answer if it's there.