The discussion revolves around the properties of the cotangent and arccotangent functions, specifically examining the equation cot|cot-1x| = cot cot-1x = x. Participants are exploring the implications of substituting specific values into this equation, particularly focusing on the case when x = -1.
The discussion is active, with participants providing insights into the properties of the cotangent and arccotangent functions. Some participants suggest that the original equation may not hold true for all values of x, while others are reconsidering their understanding of the range of the arccotangent function. There is no explicit consensus yet, but various interpretations are being explored.
There is mention of potential confusion regarding the range of the arccotangent function, with some participants noting that it is not universally established. This highlights the need for clarity on definitions and assumptions in the problem context.
Hmmmm... I think I have lost it... it's domain is ## R## and has a range ## (0, \pi)##. So ##cot^{-1}(-1)=3\pi /4## not ##-\pi /4##.Raghav Gupta said:
mooncrater said:
The standard range used for the arccotangent is (0, π). Thus the arccotangent function always returns a positive value.epenguin said:If it is not equal to the x you took, it is equal to
| (the x you took) |
and there is a | | in the problem.
I think the answer you have been given is wrong and the answer is | x | .
You seem to have been given a few wrong answers and even wrong questions, or at least at the limit thereof.