I. x is positive
y is positive
sin x is y
cos x is x
tan x is y / x
csc x is 1 / y
sec x is 1 / x
cot x is x / y

all positive

II. x is negative
y is positive
sin x is positive
cos x is negative
tan x is negative
csc x is positive
sec x is negative
cot x is negative

III. x is negative
y is negative
sin x is negative
cos x is negative
tan x is positive
csc x is negative
sec x is negative
cot x is positive

IV. x is positive
y is negative
sin x is negative
cos x is positive
tan x is negative
csc x is negative
sec x is positive
cot x is negative