Hello, kingsolomonsgrave!
$\displaystyle \text{Evaluate: }\:\cos\left(\arctan\tfrac{1}{3}\right)$
$\displaystyle \text{Let }\,\theta \,=\,\arctan\tfrac{1}{3}$
$\displaystyle \text{Then: }\:\tan\theta \:=\:\tfrac{1}{3} \:=\:\tfrac{opp}{adj}$
$\displaystyle \theta\text{ is in a right triangle with: }opp = 1,\;adj = 3$
. . $\displaystyle \text{Pythagorus says: }\:hyp = \sqrt{10}$
$\displaystyle \text{Hence: }\:\cos\theta \:=\:\tfrac{3}{\sqrt{10}}$
$\displaystyle \text{Therefore: }\:\cos\left(\arctan\tfrac{1}{3}\right) \;=\;\cos\theta \;=\;\frac{3}{\sqrt{10}}$
thanks!
So in order to work with 2*acrtan, at which stage would I multiply by 2?
would I multiply tan theta by 2 and thus take the cosine of 2/3?
I may need sleep soon, I think my brain is shutting down, this seems like it should be obvious. Sorry if im being dense