Question: How do you get $\alpha$ from $\tan{\alpha}$?

Hello,

I want to know how to obtain $\alpha$ from $\tan{\alpha}$. I mean, what is a formula (if there is one)?

I know that it is schemes where it written that if $\tan{\alpha} = 2$ then $\alpha=63.43 ^{\circ}$.

What is a formula from which we can solve for $\alpha$?

*I am not only interested in how to get $\alpha$ from $\tan{ \alpha }$. I also want to know how get $\alpha$ from $\sin{\alpha}$ and $\cos{\alpha}$.*

Answer: 
There is an inverse function called [arctangent](http://en.wikipedia.org/wiki/Inverse_trigonometric_functions). As the tangent is not one to one ($\tan (x+\pi)=\tan x)$ you have to choose which value you will return. The usual choice is that $-\frac \pi 2 \lt \arctan x \lt \frac \pi 2$
For all $x\in\mathbb R$ and $\alpha\in]-\pi/2,\pi/2[$,
$$x=\tan \alpha\iff \alpha=\arctan(x)$$
then $$\tan(\alpha)=2\iff \alpha=\arctan(2)$$