SOLUTION: What are the exact values of the six trig functions of theta when the cot theta is undefined and cos theta < 0?

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Question 715378: What are the exact values of the six trig functions of theta when the cot theta is undefined and cos theta < 0?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
What are the exact values of the six trig functions of ϴ 
when the cot(ϴ) is undefined and cos(ϴ) < 0? 

cot(ϴ) = x%2Fy 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) = y%2Fr = 0%2F1 = 0 
cos(π) = x%2Fr = %28-1%29%2F1 = -1
tan(π) = y%2Fx = 0%2F%28-1%29 = 0
sec(π) = r%2Fx = 1%2F%28-1%29 = -1
csc(π) = r%2Fy = 1%2F0 = undefined
cot(π) = x%2Fy = %28-1%29%2F0 = undefined.

Edwin