your statement is not clear. still if ∅=45 and ∅ lies in 4th quadrant. csc&cot are negative in 4th quadrant. csc ∅=1/sin ∅=1/+-sqrt(1-cos^2 ∅) =-1/sqrt(1-cos^245) =-1/sqrt(1-(1/√2)^2) =-1/√(1-1/4) =-1/√(3/4) =-2/√3 cot ∅=cos ∅/sin∅=cos315/sin315=cos(360-45)/sin (360-45) =cos 45/-sin 45=-1
