arctan(x) in terms of logs

**cragar** · Jul2-09, 09:30 PM

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

**Hurkyl** · Jul2-09, 09:31 PM

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** · Jul2-09, 09:50 PM

can i use eulers formula to do it .

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

**arildno** · Jul3-09, 05:03 AM

Correct.

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

**cragar** · Jul3-09, 12:34 PM

what quadratic

**HallsofIvy** · Jul3-09, 01:29 PM

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

**cragar** · Jul4-09, 02:25 AM

oh i see