What are the exact values of the six trig functions of ϴ 
when the cot(ϴ) is undefined and cos(ϴ) < 0? 

cot(ϴ) =  which is undefined when y=0, which are at the 
unit circle points (0,0), where ϴ = 0 and (-1,0) where ϴ = π.
cos(0) = 1 and cos(π) = -1, so since cos(ϴ) is < 0, ϴ must be π.
r = 1 on the unit circle:

sin(π) =  =  = 0 
cos(π) =  =  = -1
tan(π) =  =  = 0
sec(π) =  =  = -1
csc(π) =  =  = undefined
cot(π) =  =  = undefined.

Edwin