Trig Problem

**Erzenwald** · October 1st 2008, 11:51 AM

Need help with this:

tan(pi/2 + arctan(1/2))

Cheers!

**Moo** · October 1st 2008, 12:13 PM

Hello,

Originally Posted by Erzenwald

Need help with this:

tan(pi/2 + arctan(1/2))

Cheers!

Here is my way but you can do the way you want...

$\tan(x)=\frac{\sin(x)}{\cos(x)}$

$\sin \left(\tfrac \pi 2+x\right)=\cos(x)$
$\cos \left(\tfrac \pi 2+x\right)=-\sin(x)$
(you can check it on a unit circle)

Therefore $\tan \left(\tfrac \pi 2+x\right)=\frac{\cos(x)}{-\sin(x)}=-\frac{1}{\tan(x)}$

So $\tan \left(\tfrac \pi 2+\arctan \left(\tfrac 12\right)\right)=-\frac{1}{\tan(\arctan \left(\tfrac 12\right))}=-\frac{1}{\tfrac 12}=\boxed{-2}$

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