1. ## Cot/Arctan

Math homework is not going too well...

1. cot (arctan [sq. rt.]3/x)

Any and all help is appreciated. Thanks.

2. I hope this is clear

Good luck.

3. two things you need to do this:
1) $\displaystyle \cot{x}=\frac{1}{\tan{x}}$
2) $\displaystyle \tan [\tan^-1(x)]=x$

and so we have...

$\displaystyle \cot \left[ \tan^{-1} \left(\frac{\sqrt{3}}{x}\right) \right]$

$\displaystyle =\frac{1}{\tan \left[ \tan^{-1} \left(\frac{\sqrt{3}}{x}\right) \right]}$

$\displaystyle =\frac{1}{\frac{\sqrt{3}}{x}}$

$\displaystyle =\frac{x}{\sqrt{3}}=\frac{\sqrt{3}x}{3}$

4. Hello, TheHardcoreDave!

$\displaystyle 1)\;\cot\left[\arctan\left(\frac{\sqrt{3}}{x}\right)\right]$

We have: . $\displaystyle \cot\underbrace{\left[\arctan\left(\frac{\sqrt{3}}{x}\right)\right]}_{\text{some angle }\theta}$

Then: .$\displaystyle \theta \:=\:\arctan\left(\frac{\sqrt{3}}{x}\right)\quad\R ightarrow\quad \tan\theta \:=\:\frac{\sqrt{3}}{x} \:=\:\frac{opp}{adj}$

$\displaystyle \theta$ is in a right triangle with: $\displaystyle opp = \sqrt{3},\;adj = x$
Code:
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*  |
*     |  _
*        | √3
*           |
* θ            |
* - - - - - - - - *
x

Now . . . what is $\displaystyle \cot\theta$ ?