# Arctan(x) in terms of logs

my math teacher said that the arctan can be setup in terms of logs
does any one know how to do this.

Hurkyl
Staff Emeritus
Gold Member
Solve tan(y)=x. (Prerequisite: you must know how to write tan(y) in terms of exponentials)

Other methods are possible (e.g. antidifferentiate f(x)=1/(1+x²)), but there are more technical details involved.

can i use eulers formula to do it .

so would it be [(e^(ix)-e^(-ix)]/[(ie^(ix)+ie^(-ix))] = tan(x)

Last edited:
arildno
Homework Helper
Gold Member
Dearly Missed
Correct.

You'll need to solve a quadratic in the process.

HallsofIvy
$tan x= \frac{e^x- e^{-x}}{e^x+ e^{-x}}= y$
First multiply on both sides of the equation by $e^x+ e^{-x}$.
Then multiply both sides o the equation by $e^x$