Determine if each of the following is true or false. If false, give a counterexample.
Arccot (cot x) = x for all x
[tex]cot= 1/tan x[/tex]
Principal values of tan are -90 degrees <x <90 degrees
Capitalization of trig function indicates a function with restricted domain
The Attempt at a Solution
I figured since the cot = 1/tan, it would still have an infinite domain and range.
By that same thinking, the Cot would have the same domain and range as the Tan, -90 degrees < x <90 degrees.
But, we dont have Cot, we have the inverse of the Cot. So, do I just switch the x and y values?
I.e., the x values become infinity, and the y values become -90 degrees < x <90 degrees?
If so, does this make the equation true?