How can arctan(x) be expressed using logs?

[cragar]

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

 

[Hurkyl]

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.

 

[cragar]

can i use eulers formula to do it .

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

 

[arildno]

Correct.

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

 

[cragar]

what quadratic

 

[HallsofIvy]

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 $e^x$

 

[cragar]

oh i see