Difference between arctan(x) and cot(x)

1. Jul 20, 2009

paridiso

If arctan(x) = tan(x)^-1 and since tan(x) = sin(x)/cos(x) is not arctan(x) = cot(x). I know something's not right here but what is it?

Thanks.

2. Jul 20, 2009

rock.freak667

No no.
Cot(x)=1/tan(x)

arctan(x)=tan-1(x) $\neq$1/tan(x)

3. Jul 21, 2009

RoyalCat

Just to clarify, that notation doesn't mean the multiplicative inverse in this context, but the inverse function.

$$tan(x)=y$$
$$Arctan(y)=x$$
With whatever restrictions are necessary so that those are functions and not just relations.