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## Homework Statement

Determine if each of the following is true or false. If false, give a counterexample.

Arccot (cot x) = x for all x

## Homework Equations

[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?