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I need to find $\arctan(3)$ and before this, I'm asked to find the Maclaurin series for $\arctan(x)$, so I know they must be related. But $\arctan(x)$ is defined with $x \in [-1,1]$ so what can I do?

Bernard
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Lola
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  • No, arctan is defined on all of $\Bbb R$. You're thinking of arcsine and arccosine. – Arthur Jan 20 '18 at 19:52
  • First of all, do you know the $\arctan$ series? Do that first – Dylan Jan 20 '18 at 19:56
  • I'm thinking of using maclaurin to write acrtg 3 but I can't since this series is only defined on the above.I now thought of writing arctg /x as pi/-arctx – Lola Jan 20 '18 at 19:56
  • @dylan yes I know it,is it correct if I do as I said above? – Lola Jan 20 '18 at 19:57

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Not exactly: $\arctan x$ is defined for all $x$, but the radius of convergence of its Maclaurin series is equal to $1$.

You may reduce the problem to this case, using the relation $$\arctan x+\arctan \frac1x=\begin{cases}\dfrac\pi 2&\text{if }x>0, \\[1ex]-\dfrac\pi 2&\text{if }x<0.\end{cases}$$

Bernard
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