Arctan(x) in terms of logs

1. Jul 2, 2009

cragar

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

2. Jul 2, 2009

Hurkyl

Staff Emeritus
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.

3. Jul 2, 2009

cragar

can i use eulers formula to do it .

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

Last edited: Jul 2, 2009
4. Jul 3, 2009

arildno

Correct.

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

5. Jul 3, 2009

6. Jul 3, 2009

HallsofIvy

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

7. Jul 4, 2009

oh i see